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In this paper, by using Riordan arrays and a particular model of lattice paths, we are able to generalize in several ways an identity proposed by Lou Shapiro by giving both an algebraic and a combinatorial proof. The identities studied in this paper allow us to move from an arithmetic progression, and other C-finite sequences, to a geometric progression in terms of Riordan array transformations and vice versa, via the Riordan array inverse. [ABSTRACT FROM AUTHOR]

This paper presents a data mining methodology to analyze the careers of University graduated students. We present different approaches based on clustering and sequential patterns techniques in order to identify strategies for improving the performance of students and the scheduling of exams. We introduce an ideal career as the career of an ideal student which has taken each examination just after the end of the corresponding course, without delays. We then compare the career of a generic student with the ideal one by using the different techniques just introduced. Finally, we apply the methodology to a real case study and interpret the results which underline that the more students follow the order given by the ideal career the more they get good performance in terms of graduation time and final grade. [ABSTRACT FROM AUTHOR]

Using the inverse limit tool, we obtain the Riordan group in its infinite and bi-infinite representations from groups of finite Riordan matrices. We define two different reflections for bi-infinite Riordan matrices. Employing these definitions, we give answers to the problems D ⊥ = D and D ⋄ = D in the Riordan group. So, we describe the self-complementary and self-dual Riordan matrices. [ABSTRACT FROM AUTHOR]

Abstract: Historically, there exist two versions of the Riordan array concept. The older one (better known as recursive matrix) consists of bi-infinite matrices ( implies ), deals with formal Laurent series and has been mainly used to study algebraic properties of such matrices. The more recent version consists of infinite, lower triangular arrays ( implies ), deals with formal power series and has been used to study combinatorial problems. Here we show that every Riordan array induces two characteristic combinatorial sums in three parameters . These parameters can be specialized and generate an indefinite number of other combinatorial identities which are valid in the bi-infinite realm of recursive matrices. [Copyright &y& Elsevier]