| Autor: |
Brendan McKay, Jeanette McLeod, Ian Wanless |
| Zdroj: |
Designs, Codes & Cryptography; Sep2006, Vol. 40 Issue 3, p269-284, 16p |
| Abstrakt: |
Abstract A Latin Square of order n is an n × n array of n symbols, in which each symbol occurs exactly once in each row and column. A transversal is a set of n entries, one selected from each row and each column of a Latin Square of order n such that no two entries contain the same symbol. Define T(n) to be the maximum number of transversals over all Latin squares of order n. We show that  for n ≥ 5, where b ≈ 1.719 and c ≈ 0.614. A corollary of this result is an upper bound on the number of placements of n non-attacking queens on an n × n toroidal chess board. Some divisibility properties of the number of transversals in Latin squares based on finite groups are established. We also provide data from a computer enumeration of transversals in all Latin Squares of order at most 9, all groups of order at most 23 and all possible turn-squares of order 14. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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