Combinatorics Advances by S. Ajoodani-Namini, G. B. Khosrovshahi (auth.), Charles J.

By S. Ajoodani-Namini, G. B. Khosrovshahi (auth.), Charles J. Colbourn, Ebadollah S. Mahmoodian (eds.)

On March 28~31, 1994 (Farvardin 8~11, 1373 through Iranian calendar), the Twenty­ 5th Annual Iranian arithmetic convention (AIMC25) was once held at Sharif collage of know-how in Tehran, Islamic Republic of Iran. Its sponsors in~ eluded the Iranian Mathematical Society, and the dept of Mathematical Sciences at Sharif college of know-how. one of the keynote audio system have been Professor Dr. Andreas costume and Professor Richard ok. man. Their plenary lec~ tures on combinatorial subject matters have been complemented through invited and contributed lectures in a Combinatorics consultation. This e-book is a suite of refereed papers, submitted essentially via the contributors after the convention. the subjects coated are assorted, spanning a variety of combinatorics and al~ lied parts in discrete arithmetic. probably the power and diversity of the pa~ pers the following function the easiest symptoms that combinatorics is advancing quick, and that the Iranian arithmetic group includes very energetic individuals. we are hoping that you just locate the papers mathematically stimulating, and look ahead to an extended and effective development of combinatorial arithmetic in Iran.

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C. 5. T. Parker, "Further results on the construction of mutually orthogonal latin squares and the falsity of Euler's conjecture", Canad. J. Math. 12 (1960), 189-203. E. J. van Rees, "More mutually orthogonal latin squares", Discrete Math. 39 (1982), 263-281. J. Colbourn, "Four MOLS of order 26", J. Comb. Math. Comb. , to appear. J. Colbourn, "Some direct constructions for incomplete transversal designs", J. Stat. Plan. Infer", to appear. J. H. Dinitz and M. Wojtas, "Thwarts in transversal designs", Des.

We present one new quasi-difference matrix as an illustration of the method. J. COLBOURN columns of a quasi-dift"erence matrix with n = 1. Hence we obtain an ITD(6, 15; 3). p. = 12, Ie = 6, u = 3, ~ = 1 and Wilson [29] went on to describe a class of quasi-dift"erence matrices that can be succinctly presented. Let q = mt + 1 and let '" be a primitive element of GF(q). Now suppose tbat a vector (al, ... ,am+d exists for which, for each 1 $ Ie < m, the differences represent the m cyclotomic classes of GF( mt + 1) (compute subscripts modulo m + 2 as needed).

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