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Superstitious belief of the number of eight as a lucky number is common among the Malaysian Chinese as its pronunciation carries the meaning of “prosperity”. Nevertheless, for the non-Chinese (i.e....

we define a new notion called inclusive lucky labeling (ILL) and study proper inclusive lucky labeling (PILL) for simple undirected graphs. We also define inclusive lucky number and proper inclusive lucky number for some simple graphs.

The number 8 is considered lucky under the Chinese culture. This paper tries to examine whether investors hold such superstitious belief in the Hong Kong Stock Exchange. Using the transaction level data, we first show that more intense net buying occurs at 8-ending lots. Next, we seek favorable evidence in support of financial complexity hypothesis and informed trading hypothesis, both of which are effective in expounding the prevalence of this biased trading behavior. Finally, we find that traders’ learning by means of information acquisition is able to alleviate the lucky-8 effect on superstitious traders.

The purpose of this paper is to examine Malaysian motorists’ willingness to pay for Chinese lucky plate numbers. Regression analyses reveal that the Chinese bidders are more likely to win and pay significantly more for the Chinese lucky numbers than their non-Chinese counterparts. Consistent with resale motive considerations, the non-Chinese bidders impose the same discount for unlucky numbers as their Chinese counterparts but do not pay a premium for the lucky numbers. We also document the influence of peer effects on the winning bid price. Specifically, Chinese bidders tend to pay more for the same plate numbers won by their peers in the previous auction, whereas both Chinese and non-Chinese bidders are less averse to the unlucky numbers if there are precedents of such ownership among their peers. Overall, our findings suggest that policymakers and marketers need to be sensitive to the subtle differences in the cultural cues of consumers in a multiracial society such as Malaysia.

The proper lucky label is based on the lucky label to make the color sum of any two adjacent vertices are different. In this paper we determined the proper lucky number of cartesian product, direct product and semi-product of two path.

The labeling is said to be lucky labeling of the graph if the vertices of the graph are labeled by natural number with satisfying the condition that sum of labels over the adjacent of the vertices in the graph are not equal, and if vertices are isolated vertex, then the sum of the vertex is zero. The least natural number which labeled the graph is the lucky number. The lucky number of graph \(G\) is denoted by \(\eta \left( G \right)\). The labeling is defined as proper labeling if the vertices of the graph are labeled by natural number with fulfilling the condition that label of adjacent vertices is not the same. The labeling is defined as proper lucky labeling if labeling is proper and also lucky. The proper lucky number of graph \(G\) is denoted by \(\eta_{p} \left( G \right)\). Here, we obtain a proper lucky number for complete bipartite graph \(K_{m,n}\), friendship graph \(F_{n}\) and certain book graph such as triangular book graph \(B_{3}^{t}\) and rectangular book graph \(B_{4}^{t}\).

This game-based activity prompts students to explore the structure of multiplication, experiment with the distributive property, and begin investigating prime numbers.

Purpose Numerical superstition is well-known in Asian countries and can influence decision-making in many markets, from financial investment to purchasing a house. This study aims to determine the house price effects of superstition and understand if these have changed over time. Design/methodology/approach Using sales transactions of freestanding houses in Auckland, New Zealand, the authors use hedonic price analysis to investigate whether superstitious beliefs associated with lucky and unlucky house numbers affect property values. Findings The analysis reveals ethnic Chinese buyers in Auckland displayed superstitious home buying behaviour in the period 2003-2006 by attributing value to homes with street addresses starting or ending with the lucky number eight. However, this willing to pay higher prices for lucky numbers was not reflected in the analysis of 2011-2015 sales transactions. The disappearance of superstition price effects may indicate that ethnic Chinese in the Auckland housing market have, over time, assimilated New Zealand’s Western culture and have become less superstitious. Originality/value Unlike previous studies, the authors parse buyers into two populations of homebuyers, ethnic Chinese and non-Chinese purchasers, and model the two groups’ housing transactions independently to more accurately establish if numerical superstition influences house prices.

Eastern versus Western culture pricing practices differ with respect to price endings; however, Eastern cultures are increasingly influenced by Western multinational corporations. At the same time, increasing antiglobalization sentiment suggests the use of localization strategies in these markets. The authors investigate whether pricing practices still differ in this new environment, examine the role of superstition, and ask whether Western brands can benefit from localizing pricing practices. They explore the use of lucky number price endings and consumer responses to such pricing strategies in Singapore, an Eastern culture that is strongly exposed to Western multinational influence. Using a content analysis of newspaper advertisements and two experiments, the authors find that superstitious pricing practices continue, especially with high-priced items and brands of Eastern (vs. Western) origin. In the experimental studies, they find that superstitious pricing has a positive effect on price attractiveness and that foreign brands that localize their prices benefit from a more positive brand attitude.

In the previous chapter we learned how to introduce mathematical concepts with definitions or as primitives. Once we introduce a new concept, we are interested in its properties, usually stated as mathematical statements. Statements are sentences that are either true or false—but not both.

Estimating the value of numerical superstitions using the hedonic regression method faces an empirical challenge to separate the superstition and non-superstition components. In Malaysia, the number of eight is a lucky number by the Chinese as its pronunciation carries the meaning of “prosperity”; while for the non-Chinese (Malay), it is a neutral number (non-superstitious). This provides a natural setting to use the nonlinear decomposition analysis to remove the non-superstition component from the superstition where the hedonic regression is not able to handle. Using a sample of car plate auction data in Malaysia, this paper estimates the value of superstition in number of eight. The value of superstition is estimated to be RM965 by the hedonic regression. The nonlinear decomposition shows that it is only around 37% to 45% of the estimated superstition value (RM965) can be attributed to superstition. This indicates that the estimation of previous studies on superstitious value of number of eight using the hedonic regression model might be subject to a substantial upward bias.

This paper investigates the extent to which the frequency distribution of the rightmost digit of stock prices is influenced by numerical superstitions. To identify the moderating variables that strengthen the superstition for numbers, we take into account factors including the amount of information, change of tick size, Chinese festivals, and bear market effect. Furthermore, we examine whether the frequency of lucky (unlucky) numbers as the final digit of prices decreases (increases) for firms with higher trading by institutional investors. The results indicate that investors in the Taiwan Stock Exchange tend to avoid number 4. Our results also find that the effects of numerical superstitions on the frequency of the final digit decrease when the amount of information increases. Investors appear to be more likely to avoid unlucky number 4 in the following four conditions: when the tick size becomes smaller, when it is one week before Chinese New Year, when it is the seventh month in the lunar calendar, and when it is in a bear market. We further document that institutional investors are not affected by numerical superstition. Moreover, our results support the notion that informed traders buy and sell more (less) actively the stocks with a lower (higher) frequency of prices ending with 4.

We use the large sieve inequality with sparse sets of moduli to prove a new estimate for exponential sums over primes. Subsequently, we apply this estimate to establish new results on the binary Goldbach problem where the primes are restricted to given arithmetic progressions.

The labeling is said to be lucky labeling of the graph if the vertices of the graph are labeled by natural number with satisfying the condition that sum of labels over the adjacent of the vertices in the graph are not equal and if vertices are isolated vertex then the sum of the vertex is zero. The least natural number which labelled the graph is the lucky number. The Lucky Number of graph G is denoted by η(G). The labeling defined as proper labeling if the vertices of the graph are labeled by natural number with fulfilling the condition that label of adjacent vertices is not the same. The labeling is defined as proper lucky labeling if labeling is proper and also lucky. The proper lucky number of graph G is denoted by η p (G). Here we obtain a lucky number and proper lucky number for family of quadrilateral snake graph such as quadrilateral snake graph, double quadrilateral snake graph, alternate quadrilateral snake graph and double alternate quadrilateral snake graph.

Using price discounts government officials receive when buying new housing units as a measure of corruption in China, we examine the effect of the anti-corruption campaign launched by the Xi Jinping administration in 2012. We find that the discounts decrease sharply after the campaign. On the other hand, we find no effect of the campaign on existing housing sales. Furthermore, we find that officials become less likely to purchase housing units with lucky numbers. Overall, the results suggest the anti-corruption campaign is effective in curbing corruption.

Of all the Chinese supernatural beliefs, name-giving, whether applied to a person or a product, is extremely important, and is often considered to be closely related to fate. To this respect, this study examined the relationship between branding practices and supernatural beliefs in Chinese corporate branding strategy for bank marketing. Analytical results demonstrated that in over 50% of cases, these brand names involved a lucky number of total strokes. Finally, we suggest that the lucky-stroke-number naming strategy can be used as a tool in Chinese brand naming. Especially marketers can achieve more effective corporate branding in the Chinese business world.

If l : V ( G ) → N is a vertex labeling of a graph G = ( V ( G ) , E ( G ) ) , then the d-lucky sum of a vertex u ∈ V(G) is d l ( u ) = d G ( u ) + ∑ v ∈ N ( u ) l ( v ) . The labeling l is a d-lucky labeling if dl(u) ≠ dl(v) for every uv ∈ E(G). The d-lucky number ηdl(G) of G is the least positive integer k such that G has a d-lucky labeling V(G) → [k]. A general lower bound on the d-lucky number of a graph in terms of its clique number and related degree invariants is proved. The bound is sharp as demonstrated with an infinite family of corona graphs. The d-lucky number is also determined for the so-called Gm,n-web graphs and graphs obtained by attaching the same number of pendant vertices to the vertices of a generalized cocktail-party graph.

We investigate whether overconfidence is affected by superstitious beliefs and whether the effect is heterogeneous according to gender. With this aim, we run a field experiment involving about 700 Italian students. According to widespread superstitions, some numbers are considered lucky while others are thought of as unlucky. In our experiment, we exploited this by randomly assigning students to numbered seats in their written exam. At the end of the examination, we asked students the grade they expected to get. We find that students tend to be overconfident about their performance at the exam and that their overconfidence is positively affected by being assigned to a lucky number. Interestingly, males and females react differently: females’ overconfidence tends to be negatively affected when assigned to unlucky numbers, while they are not affected by being assigned to lucky numbers; males are not affected by being assigned to unlucky numbers but are more overconfident when assigned to lucky numbers.

We investigate whether people are influenced to make investment decisions based on random shock signals and to what extent they do so by exploiting a unique data set from a popular Chinese lottery game with over one million observations. We first present evidence that people, as individual investors in the field, not only systematically commit the hot-hand fallacy in chasing the winners who happen to pick the lucky numbers in the latest round of the lottery game, but are also willing to bear a cost in doing so although winning the lottery is merely a random shock. We then propose a simple model to account for the observed market behaviors. We further estimate the lottery players’ willingness to pay for the random shock signals, and find that the market value of such illusion is significantly high.

An {\it additive labeling} of a graph $G$ is a function $ \ell :V(G) \rightarrow\mathbb{N}$, such that for every two adjacent vertices $ v $ and $ u$ of $ G $, $ \sum_{w \sim v}\ell(w)\neq \sum_{w \sim u}\ell(w) $ ($ x \sim y $ means that $ x $ is joined to $y$). The {\it additive number} of $ G $, denoted by $\eta(G)$, is the minimum number $k $ such that $ G $ has a additive labeling $ \ell :V(G) \rightarrow \mathbb{N}_k$. The {\it additive choosability} of a graph $G$, denoted by $\eta_{\ell}(G) $, is the smallest number $k$ such that $G$ has an additive labeling for any assignment of lists of size $k$ to the vertices of $G$, such that the label of each vertex belongs to its own list. Seamone (2012) \cite{a80} conjectured that for every graph $G$, $\eta(G)= \eta_{\ell}(G)$. We give a negative answer to this conjecture and we show that for every $k$ there is a graph $G$ such that $ \eta_{\ell}(G)- \eta(G) \geq k$. A {\it $(0,1)$-additive labeling} of a graph $G$ is a function $ \ell :V(G) \rightarrow\{0,1\}$, such that for every two adjacent vertices $ v $ and $ u$ of $ G $, $ \sum_{w \sim v}\ell(w)\neq \sum_{w \sim u}\ell(w) $. A graph may lack any $(0,1)$-additive labeling. We show that it is $ \mathbf{NP} $-complete to decide whether a $(0,1)$-additive labeling exists for some families of graphs such as perfect graphs and planar triangle-free graphs. For a graph $G$ with some $(0,1)$-additive labelings, the $(0,1)$-additive number of $G$ is defined as $ \sigma_{1} (G) = \min_{\ell \in \Gamma}\sum_{v\in V(G)}\ell(v) $ where $\Gamma$ is the set of $(0,1)$-additive labelings of $G$. We prove that given a planar graph that admits a $(0,1)$-additive labeling, for all $ \varepsilon >0 $, approximating the $(0,1)$-additive number within $ n^{1-\varepsilon} $ is $ \mathbf{NP} $-hard., Comment: 14 pages, 3 figures, Discrete Mathematics & Theoretical Computer Science

A lucky labeling of a graph G is a function @?:V(G)->N, such that for every two adjacent vertices v and u of G, @?"w"~"v@?(w) @?"w"~"u@?(w) (x~y means that x is joined to y). A lucky number of G, denoted by @h(G), is the minimum number k such that G has a lucky labeling @?:V(G)->{1,...,k}. We prove that for a given planar 3-colorable graph G determining whether @h(G)=2 is NP-complete. Also for every k>=2, it is NP-complete to decide whether @h(G)=k for a given graph G.

Superstitious beliefs affect economic activity and may have noticeable economic impacts. In China, numbers often convey certain superstitious meanings. Retailers in China manipulate digital patterns on price tags to fit consumers’ superstitious preferences. In this paper, I analyze such superstitious manipulations using a large sample of price tags from Beijing, China. I also estimate the aggregate economic impacts of superstitious manipulations of retail price tags. The analytical results and the estimations presented in this paper suggest that Chinese consumers pay extra for their superstitious beliefs when they purchase goods. Retailers are the clear winners in superstitious manipulations of digital patterns in price tags.

Suppose the vertices of a graph G were labeled arbitrarily by positive integers, and let S(v) denote the sum of labels over all neighbors of vertex v. A labeling is lucky if the function S is a proper coloring of G, that is, if we have S(u) S(v) whenever u and v are adjacent. The least integer k for which a graph G has a lucky labeling from the set {1,2,...,k} is the lucky number of G, denoted by @h(G). Using algebraic methods we prove that @h(G)=

In this paper, we will consider an arithmetical approach to the Eratosthenes sieve and to the problem of the twin primes.

Cognitive priming procedures were used to identify the unique effects that luck-related concepts have on consumer behavior. The effects of these concepts could theoretically influence behavior through the elicitation of positive affect or via temporary changes in participants' self representations of how lucky they feel. An initial experiment showed that priming Asian consumers with lucky numbers independently influenced both their perceptions of personal luck and the positive affect they reported experiencing. Subsequent experiments, however, showed that the effect of these primes on consumer behavior was mediated by momentary changes in how lucky people felt (i.e. changes in the self concept) rather than by the positive affect they were experiencing at the time. Exposing consumers to lucky numbers influenced their estimates of how likely they were to win a lottery (Experiment 2), their willingness to participate in such a lottery (Experiment 4), their evaluations of different promotional strategies (Experiment 3), and also the amount of money they were willing to invest in different financial options (Experiment 4). The effect of luck on behavior was also moderated by a person's regulatory focus.

Superstition surrounding lucky numbers is observed to affect behavior in consumer goods and investment markets alike. In paying more (less) for assets perceived to be lucky (unlucky), individuals are revealing themselves as ‘enculturated’ actors in their financial decisions. This paper develops an economic framework for identifying the value assigned to ‘luck’ and examines the effect of the numbers 8 and 4 in addresses on housing prices in Sydney, Australia. These numbers are considered exceptionally lucky and unlucky, respectively, in Chinese culture. This is the first paper to test for luck-motivated behavior in both transaction and rental housing prices. Contrary to prior studies we find no evidence of a price premium (discount) attached to the number 8 (4) in transaction prices. Rental prices, however, indicate a statistically significant premium attached to the number 8 in areas of high Asian-migrant population. We provide evidence to demonstrate that this result can not be explained by a rational expectation of future luck-motivated behavior. Taken together, these results indicate that perceptions of luck are culturally-determined and that luck provides amenity, not investment, value.

In the present work we prove a number of results about gaps between consecutive primes. The proofs need the method of Y. Zhang which led to the proof of infinitely many bounded gaps between primes. Several of the results refer to the so-called Polignac numbers which we define as those even integers which can be written in infinitely many ways as the difference of two consecutive primes. Others refer to several 60–70 years old conjecture of Paul Erdős about the distribution of the normalized gaps between consecutive primes and about the distribution of the ratio of consecutive primegaps. The methods involve an extended version of Zhangs method, a property of the GPY weights proved by the author a few years ago and other ideas as well.

Some people told me that Factor 4 could imply “factor death,” as four is a homonym of death in Chinese. They recommended Factor 8 instead, because eight is considered a lucky number as the shape of its Chinese character is a symbol of good luck. It is very difficult, however, to increase resource productivity eightfold. Knowing it to be impossible for us, we settled on Factor 5, instead of 4, and not 8.

While prime numbers are the fundamental building blocks of the integers, understanding how they are spread within the integers has turned out to be hard work. For example, the Prime Number Theorem stood as a conjecture for nearly a hundred years, and anyone who bags the Riemann Hypothesis first will be a million dollars richer. Modern cryptography assumes that the primes will retain their secrets for some time to come. In the presence of hard problems, it is tempting to employ models. A good model should provide an approximation of reality which is simple enough to understand, yet accurate enough to be useful. While there are several models for the primes, in this paper we tell the story of a beautiful and compelling probabilistic model known as the Hawkins primes. First introduced by David Hawkins in this MAGAZINE [11], the model is based on a simple variation of the sieve of Eratosthenes. Over the past fifty years, the Hawkins model has been used to predict the truth, in the strongest probabilistic sense, of results (both established and conjectured) concerning the distribution of the prime numbers, including the Twin Primes Conjecture and the Riemann Hypothesis. Also, the model (or generalizations thereof) has potential to shed light on interesting integer sequences other than the primes.