Combinatorial statistics on type-B analogues of noncrossing partitions and restricted permutations

We define type-B analogues of combinatorial statistics previously studied on noncrossing partitions and show that analogous equidistribution and symmetry properties hold in the case of type-B noncrossing partitions. We also identify pattern-avoiding classes of elements in the hyperoctahedral group which parallel known classes of restricted permutations with respect to their relations to noncrossing partitions. Key words: restricted permutations, pattern-avoidance, noncrossing partitions, signed permutations, permutation statistics, partition statistics, q-analogue AMS Classification: 05 This paper was dedicated by the author to George Andrews on the occasion of his 60th birthday. We are very sad to report that Rodica Simion died on January 7, 2000, just two days after the acceptance of this paper. We have made the few minor changes requested by the referee and are honored to present her paper here.

• Type: Journal
• Year: 2000
• Where: COMBINATORICS
• Authors: Rodica Simion
• Keywords: COMBINATORICS 2000, Noncrossing Partitions, Permutation, Type-B Noncrossing Partitions