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Найдено 6 публикаций
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Статья
Gorsky Evgeny, Mazin M. Journal of Algebraic Combinatorics. 2014. Vol. 39. No. 1. P. 153-186.
Добавлено: 9 декабря 2014
Статья
Cerulli Irelli G., Feigin E., Reineke M. Journal of Algebraic Combinatorics. 2013. Vol. 38. No. 1. P. 159-189.

We study geometric and combinatorial properties of the degenerate flag varieties of type A. These varieties are acted upon by the automorphism group of a certain representation of a type A quiver, containing a maximal torus T . Using the group action, we describe the moment graphs, encoding the zero- and one-dimensional T -orbits. We also study the smooth and singular loci of the degenerate flag varieties. We show that the Euler characteristic of the smooth locus is equal to the large Schröder number and the Poincaré polynomial is given by a natural statistics counting the number of diagonal steps in a Schröder path. As an application we obtain a new combinatorial description of the large and small Schröder numbers and their q-analogues.

Добавлено: 26 июня 2013
Статья
Burman Y. M. Journal of Algebraic Combinatorics. 2018. P. 1-20.
Добавлено: 18 октября 2018
Статья
Kuyumzhiyan K. Journal of Algebraic Combinatorics. 2009. No. 30(4). P. 515-538.
Добавлено: 8 декабря 2011
Статья
Deza A., Goldengorin B. I., Pasechnik D. Journal of Algebraic Combinatorics. 2006. No. 23. P. 197-203.
Добавлено: 31 июля 2012
Статья
Feigin E., Makhlin I. Journal of Algebraic Combinatorics. 2017. Vol. 45. No. 4. P. 1083-1110.

FFLV polytopes describe monomial bases in irreducible representations of (Formula presented.) and (Formula presented.). We study various sets of vertices of FFLV polytopes. First, we consider the special linear case. We prove the locality of the set of vertices with respect to the type A Dynkin diagram. Then we describe all the permutation vertices and after that we describe all the simple vertices and prove that their number is equal to the large Schröder number. Finally, we derive analogous results for symplectic Lie algebras. 

Добавлено: 17 февраля 2017