Records in set partitions.
Recurrence relations and two-dimensional set partitions.
Remarques sur la théorie des régions et des aspects
Restricted partitions and q-Pell numbers
In this paper, we provide new combinatorial interpretations for the Pell numbers p n in terms of finite set partitions. In particular, we identify six classes of partitions of size n, each avoiding a set of three classical patterns of length four, all of which have cardinality given by p n. By restricting the statistic recording the number of inversions to one of these classes, and taking it jointly with the statistic recording the number of blocks, we obtain a new polynomial generalization of p...
Rook theory, generalized Stirling numbers and -analogues.