Ehrhart polynomial .中学数学竞赛有个很初等的定理，叫Pick 定理，说任意一个顶点为整点的多边形面积等...
of the staircasesof McDuff-Schlenk and Frenkel-M\"uller, and we prove that another infinitestaircase arises for embeddings into the ellipsoid E(1,3/2). Our proofs relatethese staircases to a combinatorial phenomenon of independent interest called"period collapse" of the Ehrhart quasipolynomial. ...
For squares and cubes we find a complete description of their Ehrhart polynomial. For hypercubes, we compute one of the coefficients and show that there exists a simple linear relation between the other two unknown coefficients. This allows as to formulate a conjecture of what the Ehrhart ...
Let A be a subspace arrangement and let (A; t) be the characteristic polynomial of its intersection lattice L(A). We show that if the subspaces in A are taken from L(B n ), where B n is the type B Weyl arrangement, then (A; t) counts a certain set of lattice points. One can...
The Ehrhart polynomial of a convex lattice polytope counts integer points in integral dilates of the polytope. We present new linear inequalities satisfied by the coefficients of Ehrhart polynomials and relate them to known inequalities... M Beck,JA De Loera,M Develin,... - 《Integer Points...
Gathering different results from singularity theory, geometry and combinatorics, we show that the spectrum at infinity of a tame Laurent polynomial counts (weighted) lattice points in polytopes. We deduce an effective algorithm in order to compute the Ehrhart polynomial of a simplex containing the ...
We introduce a class of polytopes that we call chainlink polytopes and show that they allow us to construct infinite families of pairs of non-isomorphic rational polytopes with the same Ehrhart quasipolynomial. Our construction is based on circular fence posets, a recently introduced class of poset...
quasi-polynomialint,calledtheEhrhartquasi-polynomialofP.A periodofi P (t)isD(P),thesmallestD∈Z + suchthatD·Phas integralvertices.Often,D(P)istheminimumperiodofi P (t),but,in severalinterestingexamples,theminimumperiodissmaller.Weprove that,forfixedd,thereisapolynomialtimealgorithmwhich,given...
We present a new, complex-analytic way to compute the Ehrhart polynomial of the Birkhoff polytope, that is, the function counting the integer points in the dilated polytope. One reason to be interested in this counting function is that the leading term of the Ehrhart polynomial is--up to ...
The Ehrhart polynomial of a lattice polygon P is completely determined by the pair (b(P),i(P)) where b(P) equals the number of lattice points on the boundary and i(P) equals the number of interior lattice points. All possible pairs (b(P),i(P)) are completely described by a theor...