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On the relations of various conjectures on Latin squares and straightening coefficients

โœ Scribed by Rosa Huang; Gian-Carlo Rota

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
620 KB
Volume
128
Category
Article
ISSN
0012-365X

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โœฆ Synopsis

We begin by discussing Dinitz's conjecture. Recall that a partial Latin square of order n is an n x n array of symbols with the property that no symbol appears more than once in any row or column. While a graduate student at Ohio State University, Jeff Dinitz proposed the following conjecture.

Conjecture 1 (Dinitz, 1978). Associate to each pair (i, j) where 1 <i, j<n a set S, of size n. Then there exists a partial Latin square (aij)lGi,jan with aijESij for all pairs (i,j).

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