Euler Characteristic of the Truncated Order Complex of Generalized Noncrossing Partitions
Copyright policy )Euler Characteristic of the Truncated Order Complex of Generalized Noncrossing Partitions
The purpose of this paper is to complete the study, begun in the first author's PhD thesis, of the topology of the poset of generalized noncrossing partitions associated to real reflection groups. In particular, we calculate the Euler characteristic of this poset with the maximal and minimal elements deleted. As we show, the result on the Euler characteristic extends to generalized noncrossing partitions associated to well-generated complex reflection groups.
- University System of Ohio United States
- University of Minnesota Morris United States
- University of Vienna Austria
- Miami University United States
generalized non-crossing partitions, 1010 Mathematics, 05E15 (Primary); 05A10 05A15 05A18 06A07 20F55 (Secondary), 1010 Mathematik, root systems, chain enumeration, Exact enumeration problems, generating functions, Coxeter groups, Group Theory (math.GR), 05E15 (Primary), Chu-Vandermonde summation, Combinatorial aspects of groups and algebras, 05A10 05A15 05A18 06A07 20F55 (Secondary), Partitions of sets, reflection groups, FOS: Mathematics, Mathematics - Combinatorics, Euler characteristics, Combinatorics (math.CO), Factorials, binomial coefficients, combinatorial functions, Mathematics - Group Theory
generalized non-crossing partitions, 1010 Mathematics, 05E15 (Primary); 05A10 05A15 05A18 06A07 20F55 (Secondary), 1010 Mathematik, root systems, chain enumeration, Exact enumeration problems, generating functions, Coxeter groups, Group Theory (math.GR), 05E15 (Primary), Chu-Vandermonde summation, Combinatorial aspects of groups and algebras, 05A10 05A15 05A18 06A07 20F55 (Secondary), Partitions of sets, reflection groups, FOS: Mathematics, Mathematics - Combinatorics, Euler characteristics, Combinatorics (math.CO), Factorials, binomial coefficients, combinatorial functions, Mathematics - Group Theory
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