On the number of two-line and three-line latin rectangles— an alternative approach
نویسندگان
چکیده
منابع مشابه
Counting Three-Line Latin Rectangles
A k × n Latin rectangle is a k × n array of numbers such that (i) each row is a permutation of [n] = {1, 2, . . . , n} and (ii) each column contains distinct entries. If the first row is 12 · · ·n, the Latin rectangle is said to be reduced. Since the number k × n Latin rectangles is clearly n! times the number of reduced k× n Latin rectangles, we shall henceforth consider only reduced Latin rec...
متن کاملDivisors of the number of Latin rectangles
A k×n Latin rectangle on the symbols {1, 2, . . . , n} is called reduced if the first row is (1, 2, . . . , n) and the first column is (1, 2, . . . , k) . Let Rk,n be the number of reduced k × n Latin rectangles and m = bn/2c. We prove several results giving divisors of Rk,n. For example, (k − 1)! divides Rk,n when k ≤ m and m! divides Rk,n when m < k ≤ n. We establish a recurrence which determ...
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terms of address as an important linguistics items provide valuable information about the interlocutors, their relationship and their circumstances. this study was done to investigate the change route of persian address terms in the two recent centuries including three historical periods of qajar, pahlavi and after the islamic revolution. data were extracted from a corpus consisting 24 novels w...
15 صفحه اولThe Asymptotic Number of Latin Rectangles
1. Introduction. The problem of enumerating n by k Latin rectangles was solved formally by MacMahon [4] using his operational methods. For k = 3, more explicit solutions have been given in [1], [2], [3], and [5]. Wile further exact enumeration seems difficult, it is an easy heuristic conjecture that the number of n by k Latin rectangles is asymptotic to (-n!)'cexp (-),CY,). Because of an error,...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1982
ISSN: 0012-365X
DOI: 10.1016/0012-365x(82)90171-6