Statements (28)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
integral convex polytopes
|
| gptkbp:defines |
counts the number of integer points in dilates of a polytope
|
| gptkbp:degree |
equals the dimension of the polytope
|
| gptkbp:describes |
lattice point enumeration
|
| gptkbp:field |
gptkb:geometry
combinatorics |
| gptkbp:generalizes |
gptkb:Pick's_theorem
|
| https://www.w3.org/2000/01/rdf-schema#label |
Ehrhart polynomials
|
| gptkbp:introducedIn |
1962
|
| gptkbp:namedAfter |
gptkb:Eugène_Ehrhart
|
| gptkbp:property |
constant term is 1 if the origin is inside the polytope
coefficients have geometric interpretations Ehrhart polynomial of a d-dimensional polytope is a polynomial of degree d leading coefficient equals the volume of the polytope |
| gptkbp:relatedTo |
gptkb:Pick's_theorem
gptkb:Stanley’s_reciprocity_theorem lattice polytopes quasipolynomials |
| gptkbp:studiedBy |
gptkb:Eugène_Ehrhart
|
| gptkbp:studiedIn |
discrete mathematics
polyhedral combinatorics |
| gptkbp:usedIn |
number theory
optimization algebraic combinatorics discrete geometry |
| gptkbp:bfsParent |
gptkb:Polyhedral_Combinatorics
|
| gptkbp:bfsLayer |
7
|