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DTSTART;TZID=America/Los_Angeles:20231114T121500
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DTSTAMP:20260417T104838
CREATED:20230908T055625Z
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UID:3177-1699964100-1699967400@colleges.claremont.edu
SUMMARY:f^*-vectors of lattice polytopes (Max Hlavacek\, Pomona College)
DESCRIPTION:The Ehrhart polynomial of a lattice polytope P counts the number of integer points in the nth integral dilate of P. The f^* -vector of P\, introduced by Felix Breuer in 2012\, is the vector of coefficients of the Ehrhart polynomial with respect to the binomial coefficient basis . Similarly to h and h^* -vectors\, the f^* -vector of P coincides with the f-vector (counting faces of every dimension) of its unimodular triangulations (if they exist). We give several inequalities that hold among the coefficients of f^*-vectors of polytopes. These inequalities resemble striking similarities with existing inequalities for the coefficients of f-vectors of simplicial polytopes. Even though f^* -vectors of polytopes are not always unimodal\, we describe several families of polytopes that carry the unimodality property.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-max-hlavacek-pomona-college/
LOCATION:Roberts North 102\, CMC
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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