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DESCRIPTION: Recently\, Balletti and I proved that for the h^*-polynomial h
_0^*+h_1^*t+... of a lattice polytope\, if we assume h_3^*=0\, then (h_1^*\
, h_2^*) satisfies (i) h_2^*=0\; or (ii) h_1^* \leq 3h_2^* + 3\; or (iii) (
h_1^*\,h_2^*)=(7\,1). These conditions derive from Scott's theorem (1976)\,
who characterized the possible h^*-polynomials of 2-dimensional lattice po
lytopes\, and Scott's theorem is also essentially valid for lattice polytop
es with degree at most 2 (Treutlein (2010)). On the other hand\, we proved
that it also holds under the assumption h_3^*=0. Since the assumption h_3^*
=0 is independent of both dimension and degree of polytopes\, we call the c
onditions (i)\, (ii)\, (iii) universal. In this talk\, towards finding a ne
w universal condition\, we investigate the possibility for the polynomial h
_0^*+h_1^*t+... to be the h^*-polynomial of some lattice polytope under the
assumption that some of h_i^*'s vanish.
DTSTAMP:20181113T132000
DTSTART:20180705T141500
CLASS:PUBLIC
LOCATION:Freie Universität Berlin \n Institut für Mathematik \n Arnimallee
2\n 14195 Berlin\n Seminar Room
SEQUENCE:0
SUMMARY:Akihiro Higashitani (Kyoto Sangyo University) Finding a new univers
al condition in Ehrhart theory: (Exceptionally on THURSDAY)
UID:89455123@www.facetsofcomplexity.de
URL:http://www.facetsofcomplexity.de/monday/20180705-L-Higashitani.html
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