Five experiments were conducted to determine the effect of fat addition to dry-rolled corn (DRC) finishing diets on subacute acidosis. In Exp. 1, five ruminally fistulated steers (410 +/- 12 kg BW) were used in a 5 x 5 Latin square design. Treatments consisted of 0, 2, 4, 6, or 8% tallow added to a 50% fine-ground corn: 50% dry-rolled wheat basal challenge diet and dosed intraruminally as an ac...

This article outlines some techniques for the use of bitwise operations in programming languages C/C++ and Java. As an example, we describe an algorithm for receiving a Latin square of arbitrary order.

A complete classification of redundant sets of inequalities in the specification of the Latin Square problem of size N is proven. Related issues on variations of the same problem are discussed.

In 1998, Khodkar showed that the minimal critical set in the Latin square corresponding to the elementary abelian 2-group of order 16 is of size at most 124. Since the paper was published, improved methods for solving integer programming problems have been developed. Here we give an example of a critical set of size 121 in this Latin square, found through such methods. We also give a new upper ...

The 2010 study of the Shannon entropy of order nine Sudoku and Latin square matrices by Newton and DeSalvo [Proc. Roy. Soc. A 2010] is extended to natural magic and Latin squares up to order nine. We demonstrate that decimal and integer measures of the Singular Value sets, here named SV clans, are a powerful way of comparing different integer squares. Several complete sets of magic and Latin sq...

This paper provides constructions that prove that critical sets exist of all sizes between L ~2 J and n2;n, with the exception of rf + 1 for even n, in a latin square of order n.

In this talk I will review the concept of the biembedding of two latin squares. Of particular interest will be the regular biemedding of two isomorphic copies of the latin square corresponding to the cyclic group of order n, denoted Cn. Grannell and Griggs have shown that, for all n, a regular biembedding exists, and in addition, that the automorphism group of the regular biembedding has order ...

Every Latin square of prime or prime power order s corresponds to a polynomial in 2 variables over the finite field on s elements, called the local permutation polynomial. What characterizes this polynomial is that its restrictions to one variable are permutations. We discuss the general form of local permutation polynomials and prove that their total degree is at most 2s−4, and that this bound...

Let n and k be integers, with n > 1 and k > 0. An (n × n)/k semi-Latin square S is an n × n array, whose entries (called blocks) are k-element subsets of a set of size nk, the set of symbols of S, such that each symbol of S occurs exactly once in each row and exactly once in each column of S. Semi-Latin squares form a class of designs generalising Latin squares, and have applications in areas i...

An n × n array is avoidable if for each set of n symbols there is a Latin square on these symbols which differs from the array in every cell. We characterise all unavoidable square arrays with at most 2 symbols, and all unavoidable arrays of order at most 4. We also identify a number of general families of unavoidable arrays, which we conjecture to be a complete account of unavoidable arrays. N...