A new graph invariant arises in toric topology

Suyoung Choi; Hanchul Park

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A new graph invariant arises in toric topology

机译：复曲面拓扑中出现了新的图不变性

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摘要

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 asso-ciahedron 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.

机译：在本文中，我们介绍了在复曲面拓扑中出现的任何有限简单图的新组合不变量。我们计算与图asso-ciahedron P_（B（G））相关的真实复曲面变体的第i个（有理）贝蒂数。它可以通过纯粹的组合方法（根据图形）计算，并由a_i（G）表示。令我们惊讶的是，对于图G的特定族，我们的不变量与众所周知的组合序列（如加泰罗尼亚数和欧拉之字形数）密切相关。

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来源
《Journal of the Mathematical Society of Japan》 |2015年第2期|699-720|共22页
作者
Suyoung Choi; Hanchul Park;
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作者单位

Department of Mathematics Ajou University San 5, Woncheondong, Yeongtonggu Suwon 443-749, Korea;

School of Mathematics Korea Institute for Advanced Study (KIAS) 85 Hoegiro Dongdaemungu Seoul 130-722, Korea;

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收录信息美国《科学引文索引》(SCI);
原文格式 PDF
正文语种 eng
中图分类
关键词
graph associahedron; toric topology; real toric variety; graph invariant; poset topology; shellable poset;

机译：图关联二十面体;复曲面拓扑;真正的复曲面;图不变姿态拓扑;可脱壳的;

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A new graph invariant arises in toric topology

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