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The Alon-Tarsi constants AT(n).
3

%I #16 Oct 25 2022 10:21:33

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

%N The Alon-Tarsi constants AT(n).

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

%H Jochem Berndsen, <a href="https://research.tue.nl/en/studentTheses/three-problems-in-algebraic-combinatorics">Three problems in algebraic combinatorics</a>, Student thesis: Master, Eindhoven University of Technology, 2012.

%H A. Drisko, <a href="https://doi.org/10.37236/1366">Proof of the Alon-Tarsi Conjecture for n=(2^r)*p</a>, Electronic Journal of Combinatorics, Volume 5 (1998).

%H David G. Glynn, <a href="https://doi.org/10.1137/090773751">The Conjectures of Alon-Tarsi and Rota in Dimension Prime Minus One</a>, SIAM Journal on Discrete Mathematics, 24 (2010), 394-399.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Alon-TarsiConjecture.html">Alon-Tarsi Conjecture</a>

%H P. Zappa, <a href="https://doi.org/10.1006/aama.1996.0522">The Cayley determinant of the determinant tensor and the Alon-Tarsi conjecture</a>, Advances in Applied Mathematics, 19 (1997), 31-44. [Contains an error: see Glynn.]

%F 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.

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

%K hard,sign,more

%O 2,3

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

%E Terms a(9) and a(10) added by _Jochem Berndsen_, Jun 05 2012