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October, 2016 Periodicity and the values of the real Buchstaber invariants
Hyun Woong CHO
J. Math. Soc. Japan 68(4): 1695-1723 (October, 2016). DOI: 10.2969/jmsj/06841695


The Buchstaber invariant $s(K)$ is defined to be the maximum integer for which there is a subtorus of dimension $s(K)$ acting freely on the moment-angle complex associated with a finite simplicial complex $K$. Analogously, its real version $s_{\mathbb{R}}(K)$ can also be defined by using the real moment-angle complex instead of the moment-angle complex. The importance of these invariants comes from the fact that $s(K)$ and $s_{\mathbb{R}}(K)$ distinguish two simplicial complexes and are the source of nontrivial and interesting combinatorial tasks. The ultimate goal of this paper is to compute the real Buchstaber invariants of skeleta $K=\Delta_{m-p-1}^{m-1}$ of the simplex $\Delta^{m-1}$ by making a formula. In fact, it can be solved by integer linear programming. We also give a counterexample to the conjecture which is proposed in [6] and we provide an adjusted formula which can be thought of as a preperiodicity of some numbers related to the real Buchstaber invariants.


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Hyun Woong CHO. "Periodicity and the values of the real Buchstaber invariants." J. Math. Soc. Japan 68 (4) 1695 - 1723, October, 2016.


Published: October, 2016
First available in Project Euclid: 24 October 2016

zbMATH: 1360.57040
MathSciNet: MR3564448
Digital Object Identifier: 10.2969/jmsj/06841695

Primary: 57S17
Secondary: 90C10

Keywords: Buchstaber invariant , integer programming

Rights: Copyright © 2016 Mathematical Society of Japan

Vol.68 • No. 4 • October, 2016
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