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Advances in Combinatorial Mathematics

Format: Hardback
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, Berlin, Germany
Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Published: 18th Nov 2009
Dimensions: w 156mm h 234mm d 12mm
Weight: 444g
ISBN-10: 3642035612
ISBN-13: 9783642035616
Barcode No: 9783642035616
Synopsis
It is a pleasure for me to have the opportunity to write the foreword to this volume, which is dedicated to Professor Georgy Egorychev on the occasion of his seventieth birthday. I have learned a great deal from his creative and important work, as has the whole world of mathematics. From his life's work (so far) in having made d- tinguished contributions to ?elds as diverse as the theory of permanents, Lie groups, combinatorial identities, the Jacobian conjecture, etc., let me comment on just two of the most important of his research areas. The permanent of an nxn matrix A is Per(A)= a a ...a , (1) ? 1,i 2,i n,i 1 2 n extended over the n! permutations{i ,...,i} of{1,2,...,n}. Thus, the permanent 1 n is "like the determinant except for dropping the sign factors from the terms." H- ever by dropping those signs, one loses almost all of the friendly characteristics of determinants, such as the fact that det(AB)= det(A)det(B), the invariance under elementary row and column operations, and so forth. The permanent is a creature of multilinear algebra, rather than of linear algebra, and is much crankier to deal with in virtually all of its aspects, both theoretical and algorithmic.

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