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On the Equivalence of Kirkman-Steiner Triple Systems and Sets of Mutually Orthogonal Latin Squares

A. Hedayat, B. L. Raktoe

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Abstract

It is shown that for every Kirkman-Steiner triple system of order n = 3 (mod. 6) 1 there exists at least one pair of orthogonal Latin Squares of order n. 1. BASIC DEFINITIONS In the following we need the following concepts: (i) Let L be an n-set 1 n- 1 1 3(mod. 6). Then a Steiner triple system of order n on L is a collection of unordered triplets (x 1y 1z) 1 X 1 y 1 z in L such that every pair of distinct elements of L belongs to exactly one triple. For example:

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It is shown that for every Kirkman-Steiner triple system of order n = 3 (mod. 6) 1 there exists at least one pair of orthogonal Latin Squares of order n. 1. BASIC DEFINITIONS In the following we need the following concepts: (i) Let L be an n-set 1 n- 1 1 3(mod. 6). Then a Steiner triple system of order n on L is a collection of unordered triplets (x 1y 1z) 1 X 1 y 1 z in L such that every pair of distinct elements of L belongs to exactly one triple. For example:

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Available abstract

It is shown that for every Kirkman-Steiner triple system of order n = 3 (mod. 6) 1 there exists at least one pair of orthogonal Latin Squares of order n. 1. BASIC DEFINITIONS In the following we need the following concepts: (i) Let L be an n-set 1 n- 1 1 3(mod. 6). Then a Steiner triple system of order n on L is a collection of unordered triplets (x 1y 1z) 1 X 1 y 1 z in L such that every pair of distinct elements of L belongs to exactly one triple. For example:

Key concepts: Equivalence (formal languages), Mathematics, Combinatorics, Steiner system, Discrete mathematics

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