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SUMMARY:Andrés Vindas Meléndez (University of Kentucky)
DTSTART:20210201T200000Z
DTEND:20210201T210000Z
DTSTAMP:20260423T024519Z
UID:YUAAS/21
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/YUAAS/21/">D
 ecompositions of Ehrhart h*-Polynomials for Rational Polytopes</a>\nby And
 rés Vindas Meléndez (University of Kentucky) as part of York University 
 Applied Algebra Seminar\n\n\nAbstract\nThe Ehrhart quasipolynomial of a ra
 tional polytope P encodes the number of integer lattice points in dilates 
 of P\, and the h* -polynomial of P is the numerator of the accompanying ge
 nerating function. We provide two decomposition formulas for the h*-polyno
 mial of a rational polytope. The first decomposition generalizes a theorem
  of Betke and McMullen for lattice polytopes. We use our rational Betke--M
 cMullen formula to provide a novel proof of Stanley's Monotonicity Theorem
  for the h*-polynomial of a rational polytope. The second decomposition ge
 neralizes a result of Stapledon\, which we use to provide rational extensi
 ons of the Stanley and Hibi inequalities satisfied by the coefficients of 
 the h*-polynomial for lattice polytopes. Lastly\, we apply our results to 
 rational polytopes containing the origin whose duals are lattice polytopes
 . This is joint work with Matthias Beck (San Francisco State Univ. & FU Be
 rlin) and Ben Braun (Univ. of Kentucky).\n
LOCATION:https://researchseminars.org/talk/YUAAS/21/
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