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The Bruhat rank of a binary symmetric staircase pattern

100%

Du Z., da Fonseca C. M.

Open Mathematics

2016

tom 14

nr 1

832-840

In this work we show that the Bruhat rank of a symmetric (0,1)-matrix of order n with a staircase pattern, total support, and containing In, is at most 2. Several other related questions are also discussed. Some illustrative examples are presented.

Restricted partitions and q-Pell numbers

100%

Mansour T., Shattuck M.

Open Mathematics

2011

tom 9

nr 2

346-355

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 n. Similar considerations using the comajor index statistic yields a further generalization of the q-Pell number studied by Santos and Sills.

Ograniczanie wyników

2 Open Mathematics

1 Du Z.

1 Mansour T.

1 Shattuck M.

1 da Fonseca C. M.

1 2016

1 2011

Wyniki wyszukiwania

The Bruhat rank of a binary symmetric staircase pattern

Restricted partitions and q-Pell numbers