A065711 The Alon-Tarsi constants AT(n).

1, -1, 4, -24, 2304, 368640, 6210846720, 2086844497920, 27369126116720640000

Offset: 2

Author

Jan Siwanowicz (jansiwanowicz(AT)yahoo.com), Dec 04 2001

Keywords

• hard
• sign
• more

Comments

The extended Alon-Tarsi conjecture states AT(n)<>0 for every positive integer n. Several cases have been proved - see references.

Links

• Jochem Berndsen, Three problems in algebraic combinatorics, Student thesis: Master, Eindhoven University of Technology, 2012.
• A. Drisko, Proof of the Alon-Tarsi Conjecture for n=(2^r)*p, Electronic Journal of Combinatorics, Volume 5 (1998).
• David G. Glynn, The Conjectures of Alon-Tarsi and Rota in Dimension Prime Minus One, SIAM Journal on Discrete Mathematics, 24 (2010), 394-399.
• Eric Weisstein's World of Mathematics, Alon-Tarsi Conjecture
• P. Zappa, The Cayley determinant of the determinant tensor and the Alon-Tarsi conjecture, Advances in Applied Mathematics, 19 (1997), 31-44. [Contains an error: see Glynn.]

Crossrefs

Cf. A114631 (fdels), A114632 (fdols).

Formula

AT(n)=(fdels(n)-fdols(n))/(n-1)!, where fdels(n) and fdols(n) are the numbers of fixed diagonal even and fixed diagonal odd Latin squares, respectively.

Extensions

Terms a(9) and a(10) added by Jochem Berndsen, Jun 05 2012