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Some composition determinants
J. M. Brunat, C. Krattenthaler, A. Lascoux +1
We compute two parametric determinants in which rows and columns are indexed by compositions, where in one determinant the entries are products of binomial coefficients, while in t…
The -triangle of the generalised cluster complex
Christian Krattenthaler
The -triangle is a refined face count for the generalised cluster complex of Fomin and Reading. We compute the -triangle explicitly for all irreducible finite root systems. F…
Advanced Determinant Calculus: A Complement
Christian Krattenthaler
This is a complement to my previous article "Advanced Determinant Calculus" (Séminaire Lotharingien Combin. 42 (1999), Article B42q, 67 pp.). In the present article, I share with t…
How can we escape Thomae's relations?
Christian Krattenthaler, Tanguy Rivoal
In 1879, Thomae discussed the relations between two generic hypergeometric -series with argument 1. It is well-known since then that there are 120 such relations (including…
On the number of fully packed loop configurations with a fixed associated matching
Fabrizio Caselli, Christian Krattenthaler, Bodo Lass +1
We show that the number of fully packed loop configurations corresponding to a matching with nested arches is polynomial in if is large enough, thus essentially proving…