A new graph invariant arises in toric topology

Suyoung Choi; Hanchul Park

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arXiv · 1210.3776

A new graph invariant arises in toric topology

Suyoung Choi·Hanchul Park

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Abstract

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 and Euler characteristic of the real toric variety associated to a graph associahedron $P_{\B(G)}$. They can be calculated by a purely combinatorial method (in terms of graphs) and are named $a_i(G)$ and $b(G)$, respectively. 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. 2012-10-14. A new graph invariant arises in toric topology. https://arxiv.org/abs/1210.3776

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