The Conjectures of Alon–Tarsi and Rota in Dimension Prime Minus One

DOI10.1137/090773751zbMath1227.05095OpenAlexW2006129849WikidataQ123305127 ScholiaQ123305127MaRDI QIDQ5392900

David G. Glynn

Publication date: 15 April 2011

Published in: SIAM Journal on Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/090773751

zbMATH Keywords

permutationvector spaceLatin squaredoubly stochastic matrixCayleyhyperdeterminantbasis conjectureRota

Mathematics Subject Classification ID

Combinatorial aspects of matrices (incidence, Hadamard, etc.) (05B20) Determinants, permanents, traces, other special matrix functions (15A15) Vector and tensor algebra, theory of invariants (15A72) Orthogonal arrays, Latin squares, Room squares (05B15) Combinatorial aspects of matroids and geometric lattices (05B35) Combinatorial structures in finite projective spaces (51E20) Directed graphs (digraphs), tournaments (05C20) Vector spaces, linear dependence, rank, lineability (15A03) Stochastic matrices (15B51) Primes (11A41)

Related Items (21)

Hownotto prove the Alon-Tarsi conjecture ⋮ On computing the number of Latin rectangles ⋮ A method to construct all the paving matroids over a finite set ⋮ Permanent versus determinant: Not via saturations ⋮ Girth conditions and Rota's basis conjecture ⋮ Parity of sets of mutually orthogonal Latin squares ⋮ Rota's basis conjecture for matroids with density close to one ⋮ Stability of the Levi-Civita tensors and an Alon-Tarsi type theorem ⋮ Integration formulas for Brownian motion on classical compact Lie groups ⋮ Square-root cancellation for the signs of Latin squares ⋮ Parity of transversals of Latin squares ⋮ Fundamental invariants of orbit closures ⋮ A condition for the existence of zero coefficients in the powers of the determinant polynomial ⋮ The odd case of Rota's bases conjecture ⋮ Isotopy graphs of Latin tableaux ⋮ A study of the representations supported by the orbit closure of the determinant ⋮ The Alon-Tarsi conjecture: a perspective on the main results ⋮ Special case of Rota's basis conjecture on graphic matroids ⋮ Connections between conjectures of Alon-Tarsi, Hadamard-Howe, and integrals over the special unitary group ⋮ Geometric complexity theory: an introduction for geometers ⋮ An online version of Rota's basis conjecture

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