TAILIEUCHUNG - Báo cáo toán học: "The disjoint m-flower intersection problem for latin squares"

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Department of Mathematic dành cho các bạn yêu thích môn toán học đề tài: The disjoint m-flower intersection problem for latin squares. | The disjoint m-flower intersection problem for latin squares James G. Lefevre School of Mathematics and Physics University of Queensland Brisbane QLD 4072 Australia j gl@ Thomas A. McCourt School of Mathematics and Physics University of Queensland Brisbane QLD 4072 Australia Submitted Sep 1 2010 Accepted Jan 18 2011 Published Feb 21 2011 Mathematics Subject Classification 05B15 Abstract An m-flower in a latin square is a set of m entries which share either a common row a common column or a common symbol but which are otherwise distinct. Two m-flowers are disjoint if they share no common row column or entry. In this paper we give a solution of the intersection problem for disjoint m-flowers in latin squares that is we determine precisely for which triples n m x there exists a pair of latin squares of order n whose intersection consists exactly of x disjoint m-flowers. 1 Introduction Intersection problems for latin squares were first considered by Fu 10 . Since then the area has been extensively investigated see 6 for a survey of results up until 1990. Subsequent results can be found in 7 8 1 3 and 9 . Intersection problems between pairs of Steiner triple systems were first considered by Lindner and Rosa 12 . Subsequently the intersection problem between pairs of Steiner triple systems V Vi and V V2 in which the intersection of V1 and V2 is composed of a number of isomorphic copies of some specified partial triple system have also been considered. Mullin Poplove and Zhu 15 considered the case where the partial triple system in question was a triangle. Furthermore Lindner and Hoffman 11 considered pairs of Steiner triple systems of order v intersecting in a v-21 -flower and some other THE ELECTRONIC JOURNAL OF COMBINATORICS 18 2011 P42 1 possibly empty set of triples Chang and Lo Faro 4 considered the same problem for Kirkman triple systems. In 5 Chee investigated the intersection problem for Steiner triple systems in which

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