Integer Points in Polyhedra — Geometry, Number Theory, Algebra, Optimization.
Barvinok, Alexander.
Integer Points in Polyhedra — Geometry, Number Theory, Algebra, Optimization. - 1st ed. - 1 online resource (210 pages) - Contemporary Mathematics ; v.374 . - Contemporary Mathematics .
Intro -- Contents -- Preface -- List of Participants -- A weighted version of quantization commutes with reduction for a toric manifold -- Coefficients and roots of Ehrhart polynomials -- Ehrhart polynomials of lattice polyhedral functions -- Lattice points, contingency tables, and sampling -- Kostka numbers and Littlewood-Richardson coefficients -- Polar decomposition and Brion's theorem -- Gröbner basis degree bounds on Tor·k[Λ](k, k)· and discrete Morse theory for posets -- Integer programming, duality and superadditive functions -- The Cayley trick and triangulations of products of simplices -- Problems from the Cottonwood Room -- Questions about Ehrhart coefficients. -- A conjecture about the Euler characteristic of algebraic varieties over the fields Fq, R, C and the division ring H. -- Lattice points in homogeneously expanding compact domains. -- Reflexive polytopes in dimension 2 and 3, and the numbers 12 and 24. -- Are smooth toric ideals quadratically generated? -- The classification of 1-point lattice tetrahedra. -- A conjecture on lattice tiles. -- Covering minima, free planes and deep holes.
9780821879641
Lattice theory -- Congresses.
Polyhedral functions -- Congresses.
Convex sets -- Congresses.
Number theory -- Congresses.
Polynomials -- Congresses.
Electronic books.
QA171.5 -- .A47 2003eb
516.3/5
Integer Points in Polyhedra — Geometry, Number Theory, Algebra, Optimization. - 1st ed. - 1 online resource (210 pages) - Contemporary Mathematics ; v.374 . - Contemporary Mathematics .
Intro -- Contents -- Preface -- List of Participants -- A weighted version of quantization commutes with reduction for a toric manifold -- Coefficients and roots of Ehrhart polynomials -- Ehrhart polynomials of lattice polyhedral functions -- Lattice points, contingency tables, and sampling -- Kostka numbers and Littlewood-Richardson coefficients -- Polar decomposition and Brion's theorem -- Gröbner basis degree bounds on Tor·k[Λ](k, k)· and discrete Morse theory for posets -- Integer programming, duality and superadditive functions -- The Cayley trick and triangulations of products of simplices -- Problems from the Cottonwood Room -- Questions about Ehrhart coefficients. -- A conjecture about the Euler characteristic of algebraic varieties over the fields Fq, R, C and the division ring H. -- Lattice points in homogeneously expanding compact domains. -- Reflexive polytopes in dimension 2 and 3, and the numbers 12 and 24. -- Are smooth toric ideals quadratically generated? -- The classification of 1-point lattice tetrahedra. -- A conjecture on lattice tiles. -- Covering minima, free planes and deep holes.
9780821879641
Lattice theory -- Congresses.
Polyhedral functions -- Congresses.
Convex sets -- Congresses.
Number theory -- Congresses.
Polynomials -- Congresses.
Electronic books.
QA171.5 -- .A47 2003eb
516.3/5