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pro vyhledávání: '"Danilov, V. I."'
This paper (written in Russian) presents a survey of new and earlier results on fine zonotopal tilings (briefly, cubillages) of cyclic zonotopes. The combinatorial theory of these objects is of interest in its own right and also has a connection to h
Externí odkaz:
http://arxiv.org/abs/1902.07156
We study certain structural properties of fine zonotopal tilings, or cubillages, on cyclic zonotopes $Z(n,d)$ of an arbitrary dimension $d$ and their relations to $(d-1)$-separated collections of subsets of a set $\{1,2,\ldots,n\}$. (Collections of t
Externí odkaz:
http://arxiv.org/abs/1810.05517
We consider three types of set-systems that have interesting applications in algebraic combinatorics and representation theory: maximal collections of the so-called strongly separated, weakly separated, and chord separated subsets of a set $[n]=\{1,2
Externí odkaz:
http://arxiv.org/abs/1805.09595
Akademický článek
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Autor:
Danilov, V. I.1 (AUTHOR) dvi@ispms.ru, Zuev, L. B.1 (AUTHOR), Gorbatenko, V. V.1 (AUTHOR), Orlova, D. V.1 (AUTHOR), Danilova, L. V.1 (AUTHOR)
Publikováno v:
Russian Physics Journal. Dec2022, Vol. 65 Issue 8, p1411-1418. 8p.
We present a list of ``local'' axioms and an explicit combinatorial construction for the regular $B_2$-crystals (crystal graphs of highest weight integrable modules over $U_q(sp_4)$). Also a new combinatorial model for these crystals is developed.
Externí odkaz:
http://arxiv.org/abs/0708.2198
Autor:
Danilov, V. I., Koshevoy, G. A.
We start with an ``algebraic'' RSK-correspondence due to Noumi and Yamada. Given a matrix $X$, we consider a pyramidal array of solid minors of $X$. It turns out that this array satisfies an algebraic variant of octahedron recurrence. The main observ
Externí odkaz:
http://arxiv.org/abs/math/0703414
Publikováno v:
J. of Algebra, 320, 2008, 3398-3424
A regular $A_n$-crystal is an edge-colored directed graph, with $n$ colors, related to an irreducible highest weight integrable module over $U_q(sl_{n+1})$. Based on Stembridge's local axioms for regular simply-laced crystals and a structural charact
Externí odkaz:
http://arxiv.org/abs/math/0612360
For simply-laced Kac-Moody algebras $\frak g$, Stembridge (2003) proposed a `local' axiomatization of crystal graphs of representations of $U_q(\frak g)$. In this paper we propose axioms for edge-2-colored graphs which characterize the crystals of in
Externí odkaz:
http://arxiv.org/abs/math/0611641