Proof of the Alon-Tarsi Conjecture for $n=2^rp$
نویسندگان
چکیده
منابع مشابه
Proof of the Alon-Tarsi Conjecture for n=2rp
The Alon-Tarsi conjecture states that for even n, the number of even latin squares of order n diiers from the number of odd latin squares of order n. Zappa 6] found a generalization of this conjecture which makes sense for odd orders. In this note we prove this extended Alon-Tarsi conjecture for prime orders p. By results of Drisko 2] and Zappa 6], this implies that both conjectures are true fo...
متن کاملProof of the Alon - Tarsi Conjecture for n = 2 rp Arthur
The Alon-Tarsi conjecture states that for even n, the number of even latin squares of order n differs from the number of odd latin squares of order n. Zappa [6] found a generalization of this conjecture which makes sense for odd orders. In this note we prove this extended Alon-Tarsi conjecture for prime orders p. By results of Drisko [2] and Zappa [6], this implies that both conjectures are tru...
متن کاملOn Extensions of the Alon-Tarsi Latin Square Conjecture
Expressions involving the product of the permanent with the (n − 1)st power of the determinant of a matrix of indeterminates, and of (0,1)-matrices, are shown to be related to an extension to odd dimensions of the Alon-Tarsi Latin Square Conjecture, first stated by Zappa. These yield an alternative proof of a theorem of Drisko, stating that the extended conjecture holds for Latin squares of odd...
متن کاملHow Not to Prove the Alon-tarsi Conjecture
The sign of a Latin square is −1 if it has an odd number of rows and columns that are odd permutations; otherwise, it is +1. Let Ln and L o n be, respectively, the number of Latin squares of order n with sign +1 and −1. The Alon-Tarsi conjecture asserts that Ln = Ln when n is even. Drisko showed that Lp+1 ≡ Lp+1 (mod p) for prime p ≥ 3 and asked if similar congruences hold for orders of the for...
متن کاملProof of the Alon-Yuster conjecture
In this paper we prove the following conjecture of Alon and Yuster. Let H be a graph with h vertices and chromatic number k. There exist constants c(H) and n0(H) such that if n¿n0(H) and G is a graph with hn vertices and minimum degree at least (1 − 1=k)hn + c(H), then G contains an H-factor. In fact, we show that if H has a k-coloring with color-class sizes h16h26 · · · 6h k , then the conject...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 1998
ISSN: 1077-8926
DOI: 10.37236/1366