The flush statistic on semistandard Young tableaux
نویسندگان
چکیده
منابع مشابه
Inversions of Semistandard Young Tableaux
A tableau inversion is a pair of entries from the same column of a row-standard tableau that lack the relative ordering necessary to make the tableau columnstandard. An i-inverted Young tableau is a row-standard tableau with precisely i inversion pairs, and may be interpreted as a generalization of (column-standard) Young tableaux. Inverted Young tableaux that lack repeated entries were introdu...
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We consider the parastatistics algebra with both parabosonic and parafermionic operators and show that the states in the universal parastatistics Fock space are in bijection with the Super Semistandard Young Tableaux (SSYT). Using deformation of the parastatistics algebra we get a monoid structure on SSYT which is a super version of the plactic monoid. 1 Parastatistics Fock Spaces The quantum d...
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We establish a combinatorial connection between the sequence (yn,k) counting the involutions on n letters with k descents and the sequence (an,k) enumerating the semistandard Young tableaux on n cells with k symbols. This allows us to exhibit an explicit formula for the integers yn,k and find combinatorial properties of the two sequences. In particular, we show that the sequences (yn,k) are not...
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Based on Schützenberger’s evacuation and a modification of jeu de taquin, we give a bijective proof of an identity connecting the generating function of reverse semistandard Young tableaux with bounded entries with the generating function of all semistandard Young tableaux. This solves Exercise 7.102 b of Richard Stanley’s book ‘Enumerative Combinatorics 2’.
متن کاملGenerating Functions for Inverted Semistandard Young Tableaux and Generalized Ballot Numbers
An inverted semistandard Young tableau is a row-standard tableau along with a collection of inversion pairs that quantify how far the tableau is from being column semistandard. Such a tableau with precisely k inversion pairs is said to be a k-inverted semistandard Young tableau. Building upon earlier work by Fresse and the author, this paper develops generating functions for the numbers of kinv...
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ژورنال
عنوان ژورنال: Comptes Rendus Mathematique
سال: 2014
ISSN: 1631-073X
DOI: 10.1016/j.crma.2014.03.007