Professor Curt Lindner, Auburn University, will give some seminars as follows: ------------------------------------------------------------------------ (1) Monday 2 August 2004, 4pm in room 50-2 "Perfect dexagon triple systems" Abstract. A dexagon triple is a configuration consisting of 6 triangles whose "inside edges" form a copy of K_4. A dexagon triple system is a pair (X,D), where D is a collection of edge disjoint dexagons which partitions 3K_n (= every pair of vertices are joined by 3 edges). If the inside copies of K_4 form a block design (with lambda=1), the dexagon triple system is said to be perfect. We show that a necessary and sufficient condition of the existence of a perfect dexagon triple system is n \equiv 1 (mod 12). [Joint work with Alex Rosa] ------------------------------------------------------------------------ (2) Thursday 5th August, 12 noon in room 67-641 "The intersection problem for maximum packings of K_n with triples, made easy" ------------------------------------------------------------------------ (3) COLLOQUIUM: DEPARTMENT OF MATHEMATICS THE UNIVERSITY OF QUEENSLAND COLLOQUIUM Monday 9 August, 3:00 pm, room 50-2 The Euler Officer Problem by Professor Curt Lindner Auburn University USA ABSTRACT: In 1782 Euler posed the following problem which has come to be known as the EULER OFFICER PROBLEM: 6 officers of the same 6 different ranks are selected from each of 6 regiments. Is it possible to arrange these 36 officers in a 6 X 6 array so that in each row and colomn of the array no two officers come from the same regiment or have the same rank? In modern day vernacular: Can the 36 ordered pairs formed from the the numbers 1,2,3,4,5 and 6 be arranged on a 6 X 6 board so that in each row and column of the array no two ordered pairs have the same first coordinate or the same second coordinate? In general, an Euler square is an arrangement of the n^2 ordered pairs formed from the numbers 1,2,3,4, ..., n on an n X n board so that no two orderd pairs in the same row or column have the same first coordinate or the same second coordinate. This is an ELEMENTARY survey of the history of constructing Euler squares. All welcome. Afternoon tea at 4pm in the Priestley tea room (67-704) after the talk. ------------------------------------------------------------------------ (4) Seminar, Thursday 12th August, 12 noon; room 63-360. "Constructing quasigroups from cycle systems" Everybody (except sociologists) knows that a Steiner triple system is equivalent to a quasigroup satisfying the three identies x^2 = x, (yx)x = y, and xy = yx. This can be generalized to 2-perfect m-cycle systems (too technical to go into here). This is a survey (fairly elementary if you've had years of training in university algebra) of the equivalence between 2-perfect m-cycle systems and quasigroups satisfying certain identies. This is actually a reasonably elementary talk. I was just kidding above. ------------------------------------------------------------------------