Signed mahonian identities on permutations with subsequence restrictions

Sen Peng Eu, Tung Shan Fu, Hsiang Chun Hsu, Hsin Chieh Liao, Wei Liang Sun

研究成果: 雜誌貢獻期刊論文同行評審

2 引文 斯高帕斯(Scopus)

摘要

In this paper, we present a number of results surrounding Caselli's conjecture on the equidistribution of the major index with sign over the two subsets of permutations of {1,2,…,n} containing respectively the word 12⋯k and the word (n−k+1)⋯n as a subsequence, under a parity condition of n and k. We derive broader bijective results on permutations containing varied subsequences. As a consequence, we obtain the signed mahonian identities on families of restricted permutations, in the spirit of a well-known formula of Gessel–Simion, covering a combinatorial proof of Caselli's conjecture. We also derive an extension of the insertion lemma of Han and Haglund–Loehr–Remmel which allows us to obtain a signed enumerator of the major-index increments resulting from the insertion of a pair of consecutive numbers in any place of a given permutation.

原文英語
文章編號105131
期刊Journal of Combinatorial Theory. Series A
170
DOIs
出版狀態已發佈 - 2020 二月

ASJC Scopus subject areas

  • 理論電腦科學
  • 離散數學和組合
  • 計算機理論與數學

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