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Polytopes and Large Counterexamples
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2019 (English)In: Experimental Mathematics, ISSN 1058-6458, E-ISSN 1944-950X, Vol. 28, no 1, p. 115-120Article in journal (Refereed) Published
Abstract [en]

In this short note, we give large counterexamples to natural questions about certain order polytopes, in particular, Gelfand–Tsetlin polytopes. Several of the counterexamples are too large to be discovered via a brute-force computer search. We also show that the multiset of hooks in a Young diagram is not enough information to determine the Ehrhart polynomial for an associated order polytope. This is somewhat counter-intuitive to the fact that the multiset of hooks always determine the leading coefficient of the Ehrhart polynomial.

Place, publisher, year, edition, pages
TAYLOR & FRANCIS INC , 2019. Vol. 28, no 1, p. 115-120
Keywords [en]
polytopes, counter-examples, hook formula, Ehrhart polynomial, Kostka coefficient
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-250885DOI: 10.1080/10586458.2017.1361367ISI: 000464579100010Scopus ID: 2-s2.0-85030153152OAI: oai:DiVA.org:kth-250885DiVA, id: diva2:1314019
Note

QC 20190507

Available from: 2019-05-07 Created: 2019-05-07 Last updated: 2019-06-11Bibliographically approved

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Alexandersson, Per

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