Inversion generating functions for signed pattern avoiding permutations
Department(s)
Natural Science
Document Type
Article
Publication Date
2-17-2017
Keywords
Generating function, Inversion statistic, Major index, Pattern avoiding permutations, Signed permutations
Abstract
We consider the classical Mahonian statistics on the set B (Σ) of signed per- mutations in the hyperoctahedral group B which avoid all patterns in Σ, where Σ is a set of patterns of length two. In 2000, Simion gave the cardinality of B (Σ) in the cases where Σ contains either one or two patterns of length two and showed that |B (Σ]| is constant whenever |Σ| = 1, whereas in most but not all instances where |Σ| = 2, |B (Σ)| = (n + 1)!. We answer an open question of Simion by providing bijections from B (Σ) to S in these cases where |B (Σ)| = (n + 1)!. In addition, we extend Simion’s work by providing a combinatorial proof in the language of signed permutations for the major index on B (21,21) and by giving the major index on D (Σ) for Σ = {21,21} and Σ = {21,21}. The main result of this paper is to give the inversion generating functions for B (Σ) for almost all sets Σ with |Σ| ≤ 2. n n n n n n n+1 n n n n
Publication Title
Electronic Journal of Combinatorics
E-ISSN
10778926
Volume
24
Issue
1
DOI
10.37236/6545
Recommended Citation
Cameron, Naiomi T. and Killpatrick, Kendra, "Inversion generating functions for signed pattern avoiding permutations" (2017). Pepperdine University, All Faculty Open Access Publications. Paper 102.
https://digitalcommons.pepperdine.edu/faculty_pubs/102
