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April, 2015 A new graph invariant arises in toric topology
Suyoung CHOI, Hanchul PARK
J. Math. Soc. Japan 67(2): 699-720 (April, 2015). DOI: 10.2969/jmsj/06720699


In this paper, we introduce new combinatorial invariants of any finite simple graph, which arise in toric topology. We compute the $i$-th (rational) Betti number of the real toric variety associated to a graph associahedron $P_{\B(G)}$. It can be calculated by a purely combinatorial method (in terms of graphs) and is denoted by $a_i(G)$. To our surprise, for specific families of the graph $G$, our invariants are deeply related to well-known combinatorial sequences such as the Catalan numbers and Euler zigzag numbers.


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Suyoung CHOI. Hanchul PARK. "A new graph invariant arises in toric topology." J. Math. Soc. Japan 67 (2) 699 - 720, April, 2015.


Published: April, 2015
First available in Project Euclid: 21 April 2015

zbMATH: 1326.57044
MathSciNet: MR3340192
Digital Object Identifier: 10.2969/jmsj/06720699

Primary: 55U10
Secondary: 05C30 , 57N65

Keywords: graph associahedron , graph invariant , poset topology , real toric variety , shellable poset , toric topology

Rights: Copyright © 2015 Mathematical Society of Japan


Vol.67 • No. 2 • April, 2015
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