A generating function for all semi-magic squares and the volume of the Birkhoff polytope

DOI10.1007/s10801-008-0155-yzbMath1187.05009arXivmath/0701866OpenAlexW1974073189WikidataQ56003271 ScholiaQ56003271MaRDI QIDQ735404

D. Kharzeev

Publication date: 21 October 2009

Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0701866

zbMATH Keywords

generating functionlattice pointsEhrhart polynomialBirkhoff polytopearborescencesemi-magic squareTodd polynomial

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) (52B05) Lattices and convex bodies in (n) dimensions (aspects of discrete geometry) (52C07) Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Orthogonal arrays, Latin squares, Room squares (05B15)

Related Items

A practical volume algorithm, Unistochastic Matrices and Related Problems, Algebraic and geometric structures inside the Birkhoff polytope, On superalgebras of matrices with symmetry properties, On flow polytopes, order polytopes, and certain faces of the alternating sign matrix polytope, A Chinese remainder theorem for partitions, Unconditional reflexive polytopes, Secular coefficients and the holomorphic multiplicative chaos, Ehrhart positivity of Tesler polytopes and Berline-Vergne's valuation, Computing with an algebraic-perturbation variant of Barvinok's algorithm, Characteristic classes of affine varieties and Plücker formulas for affine morphisms, Faces of Birkhoff Polytopes, On permutation polytopes: notions of equivalence

Uses Software

• LattE

Cites Work

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