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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…
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…
Proof of two conjectures of Zuber on fully packed loop configurations
F. Caselli, C. Krattenthaler
Two conjectures of Zuber [``On the counting of fully packed loops configurations. Some new conjectures,'' preprint] on the enumeration of configurations in the fully packed loop mo…
Descending plane partitions and rhombus tilings of a hexagon with triangular hole
Christian Krattenthaler
It is shown that the descending plane partitions of Andrews can be geometrically realized as cyclically symmetric rhombus tilings of a certain hexagon where an equilateral triangle…