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ARITHMETIC ASPECTS OF SYMMETRIC EDGE POLYTOPES
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2019 (English)In: Mathematika, ISSN 0025-5793, E-ISSN 2041-7942, Vol. 65, no 3, p. 763-784Article in journal (Refereed) Published
Abstract [en]

We investigate arithmetic, geometric and combinatorial properties of symmetric edge polytopes. We give a complete combinatorial description of their facets. By combining Grobner basis techniques, half-open decompositions and methods for interlacing polynomials we provide an explicit formula for the h*-polynomial in case of complete bipartite graphs. In particular, we show that the h*-polynomial is gamma-positive and real-rooted. This proves Gal's conjecture for arbitrary flag unimodular triangulations in this case, and, beyond that, we prove a strengthening due to Nevo and Petersen [On gamma-vectors satisfying the Kruskal-Katona inequalities. Discrete Comput. Geom. 45(3) (2011), 503 521].

Place, publisher, year, edition, pages
2019. Vol. 65, no 3, p. 763-784
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Mathematics
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URN: urn:nbn:se:kth:diva-253001DOI: 10.1112/S0025579319000147ISI: 000468462800016OAI: oai:DiVA.org:kth-253001DiVA, id: diva2:1327398
Note

QC 20190619

Available from: 2019-06-19 Created: 2019-06-19 Last updated: 2019-06-19Bibliographically approved

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Jochemko, Katharina

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