Yang-Baxter type equations and posets of maximal chains

[摘要] This paper addresses the problem of constructing higher dimensional versions of the Yang-Baxter equation from a purely combinatorial perspective. The usual Yang-Baxter equation may be viewed as the commutativity constraint on the two-dimensional faces of a permutahedron, a polyhedron which is related to the extension poset of a certain arrangement of hyperplanes and whose vertices are in 1-1 correspondence with maximal chains in the Boolean poser R-n. In this paper, similar constructions are performed in one dimension higher, the associated algebraic relations replacing the Yang-Baxter equation being similar to the permutahedron equation. The geometric structure of the poser of maximal chains;in S(al)x...xS(ak) is discussed in some derail, and cell types are Found to be classified by a poser of ''partitions of partitions'' in much the same way as those for permutahedra are classified by ordinary partitions. (C) 1997 Academic Press.

[发布日期] 1997-07-01

[效力级别]  Proceedings Paper