In mathematics, an integral polytope has an associated Ehrhart polynomial that encodes the relationship between the volume of a polytope and the number...

≥ 13, the coefficient of t in the Ehrhart polynomial of Tr is negative. This example shows that Ehrhart polynomials can sometimes have negative coefficients...

easily be computed from the leading coefficient of the Ehrhart polynomial. The Ehrhart polynomial associated with the Birkhoff polytope is only known for...

Ehrhart polynomial Exponential polynomials Favard's theorem Fibonacci polynomials Gegenbauer polynomials Hahn polynomials Hall–Littlewood polynomials...

applying a randomized polynomial-time approximation scheme for polytope volume. The Ehrhart polynomial of the order polytope is a polynomial whose values at...

Eugène Ehrhart (29 April 1906 – 17 January 2000) was a French mathematician who introduced Ehrhart polynomials in the 1960s. Ehrhart received his high...

a polytope", pp. 76–77 Diaz, Ricardo; Robins, Sinai (1997). "The Ehrhart polynomial of a lattice polytope". Annals of Mathematics. Second Series. 145...

chromatic polynomial and Ehrhart polynomial (see below), all special cases of Stanley's general Reciprocity Theorem. The chromatic polynomial P ( G , n...

polyhedra are formalized by the Ehrhart polynomials. These differ from figurate numbers in that, for Ehrhart polynomials, the points are always arranged...

Ehrhart is a surname. Notable people with the surname include: Eugène Ehrhart (1906–2000), French mathematician who introduced Ehrhart polynomials in the...

lattice is described by the polytope's Ehrhart polynomial. Formulas for some of the coefficients of this polynomial involve d( Λ {\displaystyle \Lambda }...

reciprocity theorem generalizes Ehrhart-Macdonald reciprocity for Ehrhart polynomials of rational convex polytopes. Ehrhart polynomial Stanley, Richard P. (1974)...

coordinates is called a lattice polyhedron or integral polyhedron. The Ehrhart polynomial of a lattice polyhedron counts how many points with integer coordinates...

Coxeter group Euclidean distance Homothetic center Hyperplane Lattice Ehrhart polynomial Leech lattice Minkowski's theorem Packing Sphere packing Kepler conjecture...

research mathematics, figurate numbers are studied by way of the Ehrhart polynomials, polynomials that count the number of integer points in a polygon or polyhedron...

Tyrrell B.; Woods, Kevin M. (2005), "The minimum period of the Ehrhart quasi-polynomial of a rational polytope", Journal of Combinatorial Theory, Series...

\mathbb {N} } . This is known as the Ehrhart quasi-polynomial, named after Eugène Ehrhart. Given two quasi-polynomials F {\displaystyle F} and G {\displaystyle...

polytope, including its volume and number of vertices, is encoded by its Ehrhart polynomial. Integral polytopes are prominently featured in the theory of toric...

in discrete geometry: Polyhedral combinatorics Lattice polytopes Ehrhart polynomials Pick's theorem Hirsch conjecture Opaque set Packings, coverings,...

1112/s0010437x06002193. S2CID 6955564. Mustaţă, Mircea; Payne, Sam (2005). "Ehrhart polynomials and stringy Betti numbers". Mathematische Annalen. 333 (4): 787–795...

closely related to the h*-vector for a convex lattice polytope, see Ehrhart polynomial. The h {\displaystyle \textstyle h} -vector ( h 0 , h 1 , … , h d...

Dehn–Sommerville equations relating numbers of faces; Pick's theorem and the Ehrhart polynomials, both of which relate lattice counting to volume; generating functions...

lattice is described by the polytope's Ehrhart polynomial. Formulas for some of the coefficients of this polynomial involve d(Λ) as well. In certain approaches...

{\displaystyle d} . Convex cone Algebraic geometry Number theory Ring theory Ehrhart polynomial Rational cone Toric variety Stanley, Richard P. (1986). "Two poset...

description) to combinatorial or algebraic properties (e.g., H-vector, Ehrhart polynomial, Hilbert basis, and Schlegel diagrams). There are also many visualization...

into orthoschemes – is it possible for simplices of every dimension? Ehrhart's volume conjecture: a convex body K {\displaystyle K} in n {\displaystyle...

_{n})={\frac {(n+1)^{n}}{n!}}\sim {\frac {e^{n+1}}{\sqrt {2\pi n}}}.} Ehrhart's volume conjecture is that this is the (optimal) upper bound on the volume...