Diagonal Complexes for Punctured Polygons

Autor:	Gaiane Panina
Rok vydání:	2017
Předmět:	Statistics and Probability Associahedron Combinatorics Mathematics::Combinatorics Planar Applied Mathematics General Mathematics Diagonal Fibration Regular polygon Polytope Ball (mathematics) Mathematics
Zdroj:	Journal of Mathematical Sciences. 224:335-338
ISSN:	1573-8795 1072-3374
DOI:	10.1007/s10958-017-3418-0
Popis:	It is known that taken together, all collections of nonintersecting diagonals in a convex planar n-gon give rise to a (combinatorial type of a) convex (n − 3)-dimensional polytope As n called the Stasheff polytope, or associahedron. In the paper, we act in a similar way by taking a convex planar n-gon with k labeled punctures. All collections of mutually nonintersecting and mutually nonhomotopic topological diagonals yield a complex As n,k . We prove that it is a topological ball. We also show a natural cellular fibration Asn,k → As n,k−1 . A special example is delivered by the case k = 1. Here the vertices of the complex are labeled by all possible permutations together with all possible bracketings on n distinct entries. This hints to a relationship with M. Kapranov’s permutoassociahedron.
Databáze:	OpenAIRE
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