Counting 3 by 𝑛 Latin rectangles
| Autor: | J. Q. Longyear, K. P. Bogart |
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| Rok vydání: | 1976 |
| Předmět: | |
| Zdroj: | Proceedings of the American Mathematical Society. 54:463-467 |
| ISSN: | 1088-6826 0002-9939 |
| Popis: | A k k by n n rectangular array A A is called a Latin rectangle if all the integers 1 , 2 , … , n 1,2, \ldots ,n appear in each row of A A and if k k distinct integers occur in each column of A A . The number of k k by n n Latin rectangles is unknown for k ⩾ 4 k \geqslant 4 ; Riordan has given a formula for the number of 3 3 by n n rectangles in terms of the solutions of the derangement (or displacement) problem and the menage problem. In this paper we derive an elementary formula for the number of 3 3 by n n Latin rectangles by using Möbius inversion. We include a table giving the approximate number of 3 3 by n n Latin rectangles for n ⩽ 20 n \leqslant 20 . The table has exact values for n ⩽ 11 n \leqslant 11 . |
| Databáze: | OpenAIRE |
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