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DESCRIPTION: If P is a lattice polytope (i.e.\, P is the convex hull of f
initely many integer points in R^d)\, Ehrhart's famous theorem asserts that
the integer-point counting function |mP∩Z^d| is a polynomial in the intege
r variable m. Equivalently\, the generating function \sum_{m \ge 0} |mP∩Z^d
| t^m is a rational function of the form h*(t)/(1-t)^{d+1}\; we call h*(t)
the Ehrhart h* - polynomial of P. We know several necessary conditions fo
r h*-polynomials\, including results by Hibi\, Stanley\, and Stapledon\, wh
o used an interplay of arithmetic (integer-point structure) and topological
(local h-vectors of triangulations) data of a given polytope. We introduce
an alternative ansatz to understand Ehrhart theory through the h*-polyno
mial of the boundary of a polytope\, recovering all of the above results
and their extensions for rational polytopes in a unifying manner. This i
s joint work with Esme Bajo (UC Berkeley).
DTSTAMP:20220612T124500
DTSTART:20220613T141500
CLASS:PUBLIC
LOCATION:Technische Universität Berlin\n Institut für Mathematik\n Straße d
es 17. Juni 136\n 10623 Berlin\n Room MA 041 (Ground Floor)
SEQUENCE:0
SUMMARY:Matthias Beck (San Francisco State University): Boundary h*-polynom
ials of rational polytopes
UID:107920432@www.facetsofcomplexity.de
URL:http://www.facetsofcomplexity.de/monday/20220613-L-Beck.html
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