77 research outputs found
Roots of the Ehrhart polynomial of hypersimplices
The Ehrhart polynomial of the -th hypersimplex of order
is studied. By computational experiments and a known result for , we
conjecture that the real part of every roots of the Ehrhart polynomial of
is negative and larger than if . In
this paper, we show that the conjecture is true when and that every root
of the Ehrhart polynomial of satisfies if .Comment: 18 pages, 8 figure
Two way subtable sum problems and quadratic Groebner bases
Hara, Takemura and Yoshida discuss toric ideals arising from two way subtable
sum problems and shows that these toric ideals are generated by quadratic
binomials if and only if the subtables are either diagonal or triangular. In
the present paper, we show that if the subtables are either diagonal or
triangular, then their toric ideals possess quadratic Groebner bases.Comment: 3 page
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