منابع مشابه
On the Number of Latin Squares
We (1) determine the number of Latin rectangles with 11 columns and each possible number of rows, including the Latin squares of order 11, (2) answer some questions of Alter by showing that the number of reduced Latin squares of order n is divisible by f ! where f is a particular integer close to 1 2 n, (3) provide a formula for the number of Latin squares in terms of permanents of (+1, −1)-mat...
متن کاملOn the number of transversals in latin squares
The logarithm of the maximum number of transversals over all latin squares of order n is greater than n6 (lnn + O(1)).
متن کاملThe number of Latin squares of order 11
Constructive and nonconstructive techniques are employed to enumerate Latin squares and related objects. It is established that there are (i) 2036029552582883134196099 main classes of Latin squares of order 11; (ii) 6108088657705958932053657 isomorphism classes of one-factorizations of K11,11; (iii) 12216177315369229261482540 isotopy classes of Latin squares of order 11; (iv) 147815745515804445...
متن کاملConcerning the number of mutually orthogonal latin squares
Let N(n) denote the maximum number of mutually orthogonal Latin squares of order n. It is shown that for large n,
متن کاملOn Completing Latin Squares
We present a ( 2 3 − o(1))-approximation algorithm for the partial latin square extension (PLSE) problem. This improves the current best bound of 1− 1 e due to Gomes, Regis, and Shmoys [5]. We also show that PLSE is APX-hard. We then consider two new and natural variants of PLSE. In the first, there is an added restriction that at most k colors are to be used in the extension; for this problem,...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1990
ISSN: 0097-3165
DOI: 10.1016/0097-3165(90)90015-o