منابع مشابه
The Existence of N2 Resolvable Latin Squares
An N2 resolvable latin squares is a latin square with no 2×2 subsquares that also has an orthogonal mate. In this paper we show that N2 resolvable latin squares exist for all orders n with n 6= 2, 4, 6, 8
متن کاملThe Existence of Latin Squares without Orthogonal Mates
A latin square is a bachelor square if it does not possess an orthogonal mate; equivalently, it does not have a decomposition into disjoint transversals. We define a latin square to be a confirmed bachelor square if it contains an entry through which there is no transversal. We prove the existence of confirmed bachelor squares for all orders greater than three. This resolves the existence quest...
متن کاملOn the existence of self-orthogonal diagonal Latin squares
A diagonal Latin square is a Latin square whose main diagonal and back diagonal are both transversals. A Latin square is self-orthogonal if it is orthogonal to its transpose. In an earlier paper Danhof, Phillips and Wallis considered the question of the existence of self-orthogonal diagonal Latin squares of order 10. In this paper we shall present some constructions of self-orthogonal diagonal ...
متن کاملAn Equilibrium Existence Theorem
Bewley 14, Theorem l] proved an infinite dimensional equilibrium existence theorem which is a significant extension of the classical finite dimensional theorem of Arrow and Debreu [ 11. The assumptions on technology and preferences are natural and applicable in a wide variety of cases. The proof is based on a limit argument that makes direct use of the existence of equilibrium in the finite dim...
متن کاملLifting Redundancy from Latin Squares to Pandiagonal Latin Squares
In the pandiagonal Latin Square problem, a square grid of size N needs to be filled with N types of objects, so that each column, row, and wrapped around diagonal (both up and down) contains an object of each type. This problem dates back to at least Euler. In its specification as a constraint satisfaction problem, one uses the all different constraint. The known redundancy result about all dif...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1945
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1945-08361-x