Two refined major-balance identities on 321-avoiding involutions
نویسندگان
چکیده
منابع مشابه
Refined sign-balance on 321-avoiding permutations
The number of even 321-avoiding permutations of length n is equal to the number of odd ones if n is even, and exceeds it by the n−1 2 th Catalan number otherwise. We present an involution that proves a refinement of this sign-balance property respecting the length of the longest increasing subsequence of the permutation. In addition, this yields a combinatorial proof of a recent analogous resul...
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Centrosymmetric involutions in the symmetric group S2n are permutations π such that π = π−1 and π(i) + π(2n + 1 − i) = 2n + 1 for all i, and they are in bijection with involutions of the hyperoctahedral group. We describe the distribution of some natural descent statistics on 321-avoiding centrosymmetric involutions, including the number of descents in the first half of the involution, and the ...
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Adin and Roichman proved a set of refined sign-balance identities on 321-avoiding permutations respecting the last descent of the permutations, which we call the identities of Adin–Roichman type. In thiswork,we construct a new involution onplane trees that proves refined sign-balance properties on 321-avoiding alternating permutations respecting the first and last entries of the permutations re...
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Let Tn be the set of 321-avoiding permutations of order n. Two properties of Tn are proved: (1) The last descent and last index minus one statistics are equidistributed over Tn, and also over subsets of permutations whose inverse has an (almost) prescribed descent set. An analogous result holds for Dyck paths. (2) The sign-and-last-descent enumerators for T2n and T2n+1 are essentially equal to ...
متن کاملA ug 2 01 5 Two descent statistics over 321 - avoiding centrosymmetric involutions
Centrosymmetric involutions in the symmetric group S2n are permutations π such that π = π−1 and π(i) + π(2n+1− i) = 2n+1 for all i, and they are in bijection with involutions of the hyperoctahedral group. We describe the distribution of some natural descent statistics on 321-avoiding centrosymmetric involutions, including the number of descents in the first half of the involution, and the sum o...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2015
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2015.04.002