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

ISBN-10: 0792335740

ISBN-13: 9780792335740

ISBN-10: 146133554X

ISBN-13: 9781461335542

ISBN-10: 1461335566

ISBN-13: 9781461335566

On March 28~31, 1994 (Farvardin 8~11, 1373 via Iranian calendar), the Twenty 5th Annual Iranian arithmetic convention (AIMC25) was once held at Sharif college 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 expertise. one of the keynote audio system have been Professor Dr. Andreas gown and Professor Richard ok. man. Their plenary lec~ tures on combinatorial issues have been complemented by way of invited and contributed lectures in a Combinatorics consultation. This booklet is a set of refereed papers, submitted basically by way of the individuals after the convention. the subjects lined are assorted, spanning a variety of combinatorics and al~ lied parts in discrete arithmetic. possibly the power and diversity of the pa~ pers right here function the easiest symptoms that combinatorics is advancing speedy, and that the Iranian arithmetic group comprises very energetic individuals. we are hoping that you simply locate the papers mathematically stimulating, and wait for a protracted and efficient progress of combinatorial arithmetic in Iran.

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**Sample text**

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). In other words, for a fixed Ie, if CJi+1c - CJi = ",mil+a and aj+1c - aj = ",my +tI , we find that a "1. f3 (mod m). Then form a single column of length m + 2 whose first entry is empty, and whose remaining entries are (all"" am+t). Form t columns by multiplying this column by the powers of ",m. From each of these t columns, form m + 2 columns by taking the m + 2 cyclic shifts of the column.

Let A be an OA(k,n) on the n symbols in X. On V = X x {I, ... ,k} (a set of size kn), form a set B of k-sets as follows. i' i) : I :$ i :$ k} in. B. Then let g be the partition of V whose classes are {X x {i} : I :$ i:$ k}. Then (V,g,B) is a TD(k,n). (k, n) from a TD(k, n). Thus, k MOLS of side n, a TD(k + 2, n), and an OA(k + 2, n) are all equivalent. In each of these disguises, mutually orthogonal latin squares have been extensively studied and lue central in combinatorial design theory and in experimental design theory.

Preprint, May 29 1991. [31] - - , An upper bound for the total chromatic number of dense graphs, J. Graph Theory, 16 (1992), pp. 197-203. , 125 (1994), pp. 211-218. [33] A. V. , 17 (1977), pp. 161-163. [34] A. V. Kostochka, An analogue of Shannon's estimate for complete colorings (Russian), Diskret. Anam. 30 (1977), pp. 13-22. [35] I. Krasikov and Y. , Ser. A, 29 (1990), pp. 215-224. [36] V. R. Kulli and N. S. Annigeri, Total graphs with croBBing number 1, J. Math. Phys. , 12 (1978), pp. 615-617.

### Combinatorics Advances by S. Ajoodani-Namini, G. B. Khosrovshahi (auth.), Charles J. Colbourn, Ebadollah S. Mahmoodian (eds.)

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