Cubillages of cyclic zonotopes

作者: G.A. Koshevoy , A.V. Karzanov , V.I. Danilov

DOI: 10.1070/RM9879

关键词:

摘要: This paper (written in Russian) presents a survey of new and earlier results on fine zonotopal tilings (briefly, cubillages) cyclic zonotopes. The combinatorial theory these objects is interest its own right also has connection to higher Bruhat orders, triangulations polytopes, Tamari-Stasheff posets applied the study Kadomtsev--Petviashvily equations, etc.

参考文章(14)
Jörg Rambau, Victor Reiner, A survey of the higher Stasheff-Tamari orders Springer Basel. pp. 351- 390 ,(2012) , 10.1007/978-3-0348-0405-9_18
Jacob Lurie, Higher Topos Theory ,(2009)
S. Felsner, H. Weil, A Theorem on Higher Bruhat Orders Discrete and Computational Geometry. ,vol. 23, pp. 121- 127 ,(2000) , 10.1007/PL00009485
Jörg Rambau, Triangulations of cyclic polytopes and higher Bruhat orders Mathematika. ,vol. 44, pp. 162- 194 ,(1997) , 10.1112/S0025579300012055
Steffen Oppermann, Hugh Thomas, Higher-dimensional cluster combinatorics and representation theory Journal of the European Mathematical Society. ,vol. 14, pp. 1679- 1737 ,(2012) , 10.4171/JEMS/345
P. H. Edelman, V. Reiner, Free arrangements and rhombic tilings Discrete & Computational Geometry. ,vol. 15, pp. 307- 340 ,(1996) , 10.1007/BF02711498
Stefan Felsner, nindexGunterGu”unter M. Ziegler, Zonotopes associated with higher Bruhat orders Discrete Mathematics. ,vol. 241, pp. 301- 312 ,(2001) , 10.1016/S0012-365X(01)00127-3
G. C. Shephard, Combinatorial Properties of Associated Zonotopes Canadian Journal of Mathematics. ,vol. 26, pp. 302- 321 ,(1974) , 10.4153/CJM-1974-032-5
Günter M. Ziegler, Higher bruhat orders and cyclic hyperplane arrangements Topology. ,vol. 32, pp. 259- 279 ,(1993) , 10.1016/0040-9383(93)90019-R
Alexander Postnikov, Pavel Galashin, Purity and separation for oriented matroids arXiv: Combinatorics. ,(2017)