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r-Stable hypersimplices
Univ Kentucky, Dept Math, Lexington, KY 40506 USA..
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2018 (English)In: Journal of combinatorial theory. Series A (Print), ISSN 0097-3165, E-ISSN 1096-0899, Vol. 157, p. 349-388Article in journal (Refereed) Published
Abstract [en]

Hypersimplices are well-studied objects in combinatorics, optimization, and representation theory. For each hypersimplex, we define a new family of subpolytopes, called r-stable hypersimplices, and show that a well-known regular unimodular triangulation of the hypersimplex restricts to a triangulation of each r-stable hypersimplex. For the case of the second hypersimplex defined by the two-element subsets of an n-set, we provide a shelling of this triangulation that sequentially shells each r-stable sub-hypersimplex. In this case, we utilize the shelling to compute the Ehrhart h*-polynomials of these poly topes, and the hypersimplex, via independence polynomials of graphs. For one such r-stable hypersimplex, this computation yields a connection to CR mappings of Lens spaces via Ehrhart-MacDonald reciprocity.

Place, publisher, year, edition, pages
ACADEMIC PRESS INC ELSEVIER SCIENCE , 2018. Vol. 157, p. 349-388
Keywords [en]
r-stable hypersimplex, Hypersimplex, Triangulation, Ehrhart h*-vector, Unimodal, Shelling
National Category
Geometry
Identifiers
URN: urn:nbn:se:kth:diva-227205DOI: 10.1016/j.jcta.2018.03.002ISI: 000430264400016Scopus ID: 2-s2.0-85043525626OAI: oai:DiVA.org:kth-227205DiVA, id: diva2:1210793
Note

QC 20180529

Available from: 2018-05-29 Created: 2018-05-29 Last updated: 2018-05-29Bibliographically approved

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Solus, Liam

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  • apa
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  • nn-NO
  • nn-NB
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  • Other locale
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Output format
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