By Ams-asl Joint Special Session on Interac, Alexandre Borovik

ISBN-10: 0821836188

ISBN-13: 9780821836187

ISBN-10: 2419892232

ISBN-13: 9782419892230

Because the pioneering works of Novikov and Maltsev, workforce idea has been a trying out flooring for mathematical good judgment in its many manifestations, from the speculation of algorithms to version idea. The interplay among common sense and staff idea resulted in many in demand effects which enriched either disciplines. This quantity displays the most important issues of the yankee Mathematical Society/Association for Symbolic common sense Joint precise consultation (Baltimore, MD), Interactions among good judgment, crew idea and computing device technology. incorporated are papers dedicated to the improvement of suggestions used for the interplay of staff concept and good judgment. it's compatible for graduate scholars and researchers drawn to algorithmic and combinatorial workforce idea. A supplement to this paintings is quantity 349 within the ""AMS"" sequence, ""Contemporary arithmetic, Computational and Experimental workforce Theory"", which arose from an identical assembly and concentrates at the interplay of crew concept and laptop technology

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**Sample text**

21 is taken from [36]. The q-Schur algebras were introduced by Dipper and James, [21]. 22 see [36]. 22 and the remaining sections concern topics to be described in more detail in the main body of the text. 22, is due to Dipper and James, [20]. 1. Exterior Algebra The purpose of this chapter is to give a basis of A(n) consisting of bideterminants. This basis is a q-analogue of the basis given by several authors in the classical case: see Mead, [67]; Doubilet, Rota and Stein, [43]; De Concini, Eisenbud and Procesi, [17]; and Green, [52].

For a set X we write Sym(X) for the group of permutations of X. Thus Sym(r) = Sym[1, r], for r > 1. We fix a positive integer n. Let R be a commutative ring and q E R. Let A(n) = AR,q(n) be the R-algebra generated by cij, 1 < i, j < n, subject to the relations AI CirCis = CisCir All Cjrcis=gciscjr AIII CjsCir = CirCjs + (q - 1)ciscjr for all i, r, s; for alli

We shall often write i E I(n, r) as the sequence (i1, ... , ir) (where is = i(a), 1 < a < r). Let i = (i1 i ... , ir) E I(n, r). We define ei = ei, ® ® eir E E®'* and vi = vi, ® ® vi,. E V®'. We define ei = ei, A A eir E AE, the image of ei under the natural map E®r -> ArE and define vi = vi, A A vi, E A' V, the image of vi under the natural map V®r->ArV. We write P = P(n) for a certain set of sequences of non-negative integers. We define P to be 0 together with sequences a = (a1, ... , am), for E P we some positive integer m, with entries a1, ...

### Groups, Languages, Algorithms: Ams-asl Joint Special Session On Interactions Between Logic, Group Theory, And Computer Science, January 16-19, 2003, Baltimore, Maryland by Ams-asl Joint Special Session on Interac, Alexandre Borovik

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