Combinatorial generation algorithms for the set defined by central polygonal numbers.

In this paper, we study the combinatorial set of pieces formed when slicing a disk with a given number of straight cuts. The cardinality function of this combinatorial set is described by the central polygonal numbers. Using the obtained cardinality function, we construct the corresponding AND/OR tree structure and determine a bijection between the set of variants of the AND/OR tree and the considered combinatorial set. In addition, we develop ranking and unranking algorithms for the combinatorial set. [ABSTRACT FROM AUTHOR]