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Total occurrence statistics on restricted permutations | Alexander Burstein
; Sergi Elizalde
; | Date: |
14 May 2013 | Abstract: | We study the total number of occurrences of several vincular (also called
generalized) patterns and other statistics, such as the major index and the
Denert statistic, on permutations avoiding a pattern of length 3, extending
results of Bona (2010, 2012) and Homberger (2012). In particular, for
2-3-1-avoiding permutations, we find the total number of occurrences of any
vincular pattern of length 3. In some cases the answer is given by simple
expressions involving binomial coefficients. The tools we use are bijections
with Dyck paths, generating functions, and block decompositions of
permutations. | Source: | arXiv, 1305.3177 | Services: | Forum | Review | PDF | Favorites |
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