Subgroup Lattices And Symmetric Functions

Author : Lynne M. Butler
Publisher : American Mathematical Soc.
ISBN 13 : 082182600X
Total Pages : 173 pages
Book Rating : 4.03/5 ( download)

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Download or read book Subgroup Lattices and Symmetric Functions written by Lynne M. Butler and published by American Mathematical Soc.. This book was released on 1994 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents foundational research on two approaches to studying subgroup lattices of finite abelian p-groups. The first approach is linear algebraic in nature and generalizes Knuth's study of subspace lattices. This approach yields a combinatorial interpretation of the Betti polynomials of these Cohen-Macaulay posets. The second approach, which employs Hall-Littlewood symmetric functions, exploits properties of Kostka polynomials to obtain enumerative results such as rank-unimodality. Butler completes Lascoux and Schützenberger's proof that Kostka polynomials are nonnegative, then discusses their monotonicity result and a conjecture on Macdonald's two-variable Kostka functions.

Author : Lynne L. Butler
Publisher :
ISBN 13 :
Total Pages : 160 pages
Book Rating : 4.83/5 ( download)

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Download or read book Subgroup Lattices and Symmetric Functions written by Lynne L. Butler and published by . This book was released on 1994 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Roland Schmidt
Publisher : Walter de Gruyter
ISBN 13 : 3110868644
Total Pages : 589 pages
Book Rating : 4.47/5 ( download)

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Download or read book Subgroup Lattices of Groups written by Roland Schmidt and published by Walter de Gruyter. This book was released on 2011-07-20 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany

Author : Alexander Lubotzky
Publisher : Birkhäuser
ISBN 13 : 3034889658
Total Pages : 463 pages
Book Rating : 4.50/5 ( download)

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Download or read book Subgroup Growth written by Alexander Lubotzky and published by Birkhäuser. This book was released on 2012-12-06 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: Award-winning monograph of the Ferran Sunyer i Balaguer Prize 2001. Subgroup growth studies the distribution of subgroups of finite index in a group as a function of the index. In the last two decades this topic has developed into one of the most active areas of research in infinite group theory; this book is a systematic and comprehensive account of the substantial theory which has emerged. As well as determining the range of possible 'growth types', for finitely generated groups in general and for groups in particular classes such as linear groups, a main focus of the book is on the tight connection between the subgroup growth of a group and its algebraic structure. A wide range of mathematical disciplines play a significant role in this work: as well as various aspects of infinite group theory, these include finite simple groups and permutation groups, profinite groups, arithmetic groups and Strong Approximation, algebraic and analytic number theory, probability, and p-adic model theory. Relevant aspects of such topics are explained in self-contained 'windows'.

Author : Christian Krattenthaler
Publisher : American Mathematical Soc.
ISBN 13 : 0821826131
Total Pages : 122 pages
Book Rating : 4.33/5 ( download)

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Download or read book The Major Counting of Nonintersecting Lattice Paths and Generating Functions for Tableaux written by Christian Krattenthaler and published by American Mathematical Soc.. This book was released on 1995 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: A theory of counting nonintersecting lattice paths by the major index and its generalizations is developed. We obtain determinantal expressions for the corresponding generating functions for families of nonintersecting lattice paths with given starting points and given final points, where the starting points lie on a line parallel to [italic]x + [italic]y = 0. In some cases these determinants can be evaluated to result in simple products. As applications we compute the generating function for tableaux with [italic]p odd rows, with at most [italic]c columns, and with parts between 1 and [italic]n. Moreover, we compute the generating function for the same kind of tableaux which in addition have only odd parts. We thus also obtain a closed form for the generating function for symmetric plane partitions with at most [italic]n rows, with parts between 1 and [italic]c, and with [italic]p odd entries on the main diagonal. In each case the result is a simple product. By summing with respect to [italic]p we provide new proofs of the Bender-Knuth and MacMahon (ex-)conjectures, which were first proved by Andrews, Gordon, and Macdonald. The link between nonintersecting lattice paths and tableaux is given by variations of the Knuth correspondence.

Author : Solomon Friedberg
Publisher : American Mathematical Soc.
ISBN 13 : 0821805401
Total Pages : 167 pages
Book Rating : 4.04/5 ( download)

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Download or read book The Fundamental Lemma for the Shalika Subgroup of $GL(4)$ written by Solomon Friedberg and published by American Mathematical Soc.. This book was released on 1996 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors establish the fundamental lemma for a relative trace formula. The trace formula compares generic automorphic representations of [italic capitals]GS[italic]p(4) with automorphic representations of [italic capitals]GS(4) which are distinguished with respect to a character of the Shalika subgroup, the subgroup of matrices of 2 x 2 block form ([superscript italic]g [over] [subscript capital italic]X [and] 0 [over] [superscript italic]g). The fundamental lemma, giving the equality of the orbital integrals of the unit elements of the respective Hecke algebras, amounts to a comparison of certain exponential sums arising from these two different groups.

Author : Arne Dür
Publisher : Springer
ISBN 13 : 354039818X
Total Pages : 145 pages
Book Rating : 4.89/5 ( download)

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Download or read book Möbius Functions, Incidence Algebras and Power Series Representations written by Arne Dür and published by Springer. This book was released on 2006-11-14 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Valentina Colombo
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.19/5 ( download)

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Download or read book Some Properties of the Möbius Function in the Subgroup Lattice of the Alternating and Symmetric Groups written by Valentina Colombo and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Peter Cholak
Publisher : American Mathematical Soc.
ISBN 13 : 0821826018
Total Pages : 166 pages
Book Rating : 4.10/5 ( download)

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Download or read book Automorphisms of the Lattice of Recursively Enumerable Sets written by Peter Cholak and published by American Mathematical Soc.. This book was released on 1995 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: A version of Harrington's [capital Greek]Delta3-automorphism technique for the lattice of recursively enumerable sets is introduced and developed by reproving Soare's Extension Theorem. Then this automorphism technique is used to show two technical theorems: the High Extension Theorem I and the High Extension Theorem II. This is a degree-theoretic technique for constructing both automorphisms of the lattice of r.e. sets and isomorphisms between various substructures of the lattice.

Author : Darryl McCullough
Publisher : American Mathematical Soc.
ISBN 13 : 0821804596
Total Pages : 113 pages
Book Rating : 4.99/5 ( download)

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Download or read book Symmetric Automorphisms of Free Products written by Darryl McCullough and published by American Mathematical Soc.. This book was released on 1996 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors construct a complex [italic capital]K([italic capital]G) on which the automorphism group of [italic capital]G acts and use it to derive finiteness consequences for the group [capital Greek]Sigma [italic]Aut([italic capital]G). They prove that each component of [italic capital]K([italic capital]G) is contractible and describe the vertex stabilizers as elementary constructs involving the groups [italic capital]G[subscript italic]i and [italic]Aut([italic capital]G[subscript italic]i).