Ehrhart Series of Fractional Stable Set Polytopes of Finite Graphs

Ehrhart Series of Fractional Stable Set Polytopes of Finite Graphs c Springer Basel AG 2018 Annals of Combinatorics 22 (2018) 1-• • • Ann. Comb. 12 (2009) 479–492 Annals of Combinatorics 0218-0006/18/010001-10 https://doi.org/10.1007/s00026-018-0392-2 Annals of Combinatorics DOI *********** © Springer International Publishing AG, part of Springer Nature 2018 Ehrhart Series of Fractional Stable Set Polytopes of Finite Graphs 1 2 3 Ginji Hamano , Takayuki Hibi , and Hidefumi Ohsugi Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Suita, Osaka 565-0871, Japan u973849g@alumni.osaka-u.ac.jp Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Suita, Osaka 565-0871, Japan hibi@math.sci.osaka-u.ac.jp Department of Mathematical Sciences, School of Science and Technology, Kwansei Gakuin University, Sanda, Hyogo 669-1337, Japan ohsugi@kwansei.ac.jp Received June 29, 2016 Mathematics Subject Classification: 52B05, 52B20 Abstract. The fractional stable set polytope FRAC(G) of a simple graph G with d vertices is a rational polytope that is the set of nonnegative vectors (x , . . . , x ) satisfying x + x ≤ 1 1 d i j for every edge (i, j) of G. In this paper we show that (i) the δ-vector of a lattice polytope 2FRAC(G) is alternatingly increasing, (ii) the Ehrhart ring of http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Combinatorics Springer Journals

Ehrhart Series of Fractional Stable Set Polytopes of Finite Graphs

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Publisher
Springer International Publishing
Copyright
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Mathematics; Combinatorics
ISSN
0218-0006
eISSN
0219-3094
D.O.I.
10.1007/s00026-018-0392-2
Publisher site
See Article on Publisher Site

Abstract

c Springer Basel AG 2018 Annals of Combinatorics 22 (2018) 1-• • • Ann. Comb. 12 (2009) 479–492 Annals of Combinatorics 0218-0006/18/010001-10 https://doi.org/10.1007/s00026-018-0392-2 Annals of Combinatorics DOI *********** © Springer International Publishing AG, part of Springer Nature 2018 Ehrhart Series of Fractional Stable Set Polytopes of Finite Graphs 1 2 3 Ginji Hamano , Takayuki Hibi , and Hidefumi Ohsugi Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Suita, Osaka 565-0871, Japan u973849g@alumni.osaka-u.ac.jp Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Suita, Osaka 565-0871, Japan hibi@math.sci.osaka-u.ac.jp Department of Mathematical Sciences, School of Science and Technology, Kwansei Gakuin University, Sanda, Hyogo 669-1337, Japan ohsugi@kwansei.ac.jp Received June 29, 2016 Mathematics Subject Classification: 52B05, 52B20 Abstract. The fractional stable set polytope FRAC(G) of a simple graph G with d vertices is a rational polytope that is the set of nonnegative vectors (x , . . . , x ) satisfying x + x ≤ 1 1 d i j for every edge (i, j) of G. In this paper we show that (i) the δ-vector of a lattice polytope 2FRAC(G) is alternatingly increasing, (ii) the Ehrhart ring of

Journal

Annals of CombinatoricsSpringer Journals

Published: Jun 5, 2018

References

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