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    题名: Signed mahonian identities on permutations with subsequence restrictions
    作者: Eu, Sen-Peng;Fu, Tung-Shan;Hsu, Hsiang-Chun;Liao, Hsin-Chieh;Sun, Wei-Liang
    关键词: Signed major index;Equidistribution;Permutations with subsequence restrictions;Linear extensions;Pattern avoiding permutations;Insertion lemma
    日期: 2020-02
    上传时间: 2020-03-24 12:10:18 (UTC+8)
    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 1 2 · · · 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 and Simion, covering a combinatorial proof of Caselli’s conjecture. We also derive an extension of the insertion lemma of Haglund, Loehr, and 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.
    關聯: Journal of Combinatorial Theory Series A 170, 105131
    DOI: 10.1016/j.jcta.2019.105131
    显示于类别:[數學學系暨研究所] 期刊論文


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