Signed mahonian identities on permutations with subsequence restrictions
學年 108
學期 2
出版（發表）日期 2020-02-01
作品名稱 Signed mahonian identities on permutations with subsequence restrictions
作品名稱（其他語言）
著者 Sen-Peng Eu; Tung-Shan Fu; Hsiang-Chun Hsu; Hsin-Chieh Liao; Wei-Liang Sun
單位
出版者
著錄名稱、卷期、頁數 Journal of Combinatorial Theory Series A 170, 105131
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.
關鍵字 Signed major index;Equidistribution;Permutations with subsequence restrictions;Linear extensions;Pattern avoiding permutations;Insertion lemma
語言 en_US
ISSN 0097-3165
期刊性質 國外
收錄於 SCI
產學合作
通訊作者
審稿制度 否
國別 USA
公開徵稿
出版型式 ,電子版
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