Generalizations of Baxter's theorem and cubical homology
type: Item
instance of: scholarly article
title: Generalizations of Baxter's theorem and cubical homology
zbMATH Open document ID: 0847.57003
DOI: 10.1016/0097-3165(95)90053-5
author: Richard Ehrenborg
author: Gabor Hetyei
published in: Journal of Combinatorial Theory. Series A
publication date: 1996-10-15T00:00:00Z
review text: Consider a 3-regular planar graph. Arbitrarily assign one of four colors to each of its regions. Let \(A_1\) be the number of vertices surrounded by regions of colors 234 in clockwise order, minus the number of vertices surrounded by regions of colors 234 in counterclockwise order. Define \(A_2, A_3, A_4\) similarly. In [J. Comb. Theory 1, 375-384 (1966; Zbl 0144.45201)] \textit{G. Baxter} proved the following result: \[ \text{Theorem 1.} \quad A_1 = - A_2 = A_3 = - A_4. \] In this paper we generalize this theorem to triangulated and cubically subdivided manifolds of arbitrary dimension in several ways. From our cubical results we obtain a way to construct a cubical analogue of simplicial homology.
Mathematics Subject Classification ID: 57M15
Mathematics Subject Classification ID: 57Q15
zbMATH DE Number: 734535
zbMATH Keywords: 3-regular
zbMATH Keywords: planar graph
zbMATH Keywords: triangulated
zbMATH Keywords: cubically subdivided
zbMATH Keywords: manifolds
zbMATH Keywords: simplicial homology
MaRDI profile type: Publication
full work available at URL: 0097-3165(95)90053-5
OpenAlex ID: W2042124355
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description: scientific article; zbMATH DE number 734535