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Random partitions and asymptotic theory of symmetric groups, Hecke algebras and finite Chevalley groups
Random partitions asymptotic theory of symmetric groups Hecke algebras finite Chevalley groups
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2011/2/22
Kit meanwhile had begun to frequent the Applied Mechanics Institute. Since Prandtl’s recent discovery of the boundary layer, things over there had been hopping, with intense inquiry into matters of li...
Partitions and functional Santalo inequalities
Santalo inequalities math
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2010/11/15
We give a direct proof of a functional Santalo inequality due to Fradelizi and Meyer. This provides a new proof of the Blaschke-Santalo inequality. The argument combines a logarithmic form of the Prek...
Partitions and Partial Matchings Avoiding Neighbor Patterns
set partition partial matching neighbor alignment left nesting right nesting
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2010/12/10
We obtain the generating functions for partial matchings avoiding neighbor alignments and for partial matchings avoiding neighbor alignments and left nestings. We show that there is a bijection betwee...
Identities Derived from Noncrossing Partitions of Type B
noncrossing partition of type B Narayana polynomial of type B bijection
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2014/6/3
Based on weighted noncrossing partitions of type B, we obtain type B analogues of Coker’s identities on the Narayana polynomials. A parity reversing involution is given for the alternating sum of Nara...
Labeled Partitions and the q-Derangement Numbers
q-derangement number major index bijection partitions labeled partitions
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2014/6/3
Inspired by MacMahon's original proof of his celebrated theorem on the distribution of the major index over permutations, we give a reformulation of his argument in terms of labeled partitions. In thi...
A Major Index for Matchings and Set Partitions
tangled-diagram partition matching crossing nesting vacillating tableau
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2014/6/3
A tangled diagram on [n] = {1,..., n} is a labeled graph for which each vertex has degree at most two. The vertices are arranged in increasing order on a horizontal line and the arcs are drawn in the ...
A Major Index for Matchings and Set Partitions
tangled-diagram partition matching crossing nesting vacillating tableau
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2014/6/3
A tangled diagram on [n] = {1,..., n} is a labeled graph for which each vertex has degree at most two. The vertices are arranged in increasing order on a horizontal line and the arcs are drawn in the ...
Une identité remarquable en théorie des partitions
Une identité remarquable théorie partitions
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2010/10/29
We prove an identity about partitions, previously conjectured in the study of shifted Jack polynomials (math.CO/9903020). The proof given is using $\lambda$-ring techniques. It would be interesting t...