منابع مشابه
ON q-INTEGRALS OVER ORDER POLYTOPES
A combinatorial study of multiple q-integrals is developed. This includes a q-volume of a convex polytope, which depends upon the order of q-integration. A multiple q-integral over an order polytope of a poset is interpreted as a generating function of linear extensions of the poset. Specific modifications of posets are shown to give predictable changes in q-integrals over their respective orde...
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We express the Segre class of a monomial scheme—or, more generally, a scheme monomially supported on a set of divisors cutting out complete intersections— in terms of an integral computed over an associated body in euclidean space. The formula is in the spirit of the classical Bernstein-Kouchnirenko theorem computing intersection numbers of equivariant divisors in a torus in terms of mixed volu...
متن کاملOn double integrals over spheres
Formulae involving double integrals over spheres arise naturally in inverse scattering problems since the scattered data are measured in the space R x Sz x Sz. In this paper we derive a relation between differential forms on the space S"' x S"-' , and those on the space Z x S n-2 x S where Z is a real interval. Specifically, d( dq = sin"' 6 d6 d$ dv (t, 7) E S '-' x S '-' and (6, $, U) E Z x S"...
متن کاملGorenstein Fano Polytopes Arising from Order Polytopes and Chain Polytopes
Richard Stanley introduced the order polytope O(P ) and the chain polytope C(P ) arising from a finite partially ordered set P , and showed that the Ehrhart polynomial of O(P ) is equal to that of C(P ). In addition, the unimodular equivalence problem of O(P ) and C(P ) was studied by the first author and Nan Li. In the present paper, three integral convex polytopes Γ(O(P ),−O(Q)), Γ(O(P ),−C(Q...
متن کاملOrder-Chain Polytopes
Given two families X and Y of integral polytopes with nice combinatorial and algebraic properties, a natural way to generate new class of polytopes is to take the intersection P = P1 ∩ P2, where P1 ∈ X, P2 ∈ Y . Two basic questions then arise: 1) when P is integral and 2) whether P inherits the “old type” from P1,P2 or has a “new type”, that is, whether P is unimodularly equivalent to some poly...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2017
ISSN: 0001-8708
DOI: 10.1016/j.aim.2017.01.001