Subgroup Lattices And Symmetric Functions

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Subgroup Lattices And Symmetric Functions

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Author : Lynne M. Butler
language : en
Publisher: American Mathematical Soc.
Release Date : 1994

Subgroup Lattices And Symmetric Functions written by Lynne M. Butler and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.

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.

Subgroup Lattices And Symmetric Functions

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Author :
language : en
Publisher:
Release Date : 1995

Subgroup Lattices And Symmetric Functions written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with categories.

Subgroup Lattices And Symmetric Functions

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Author : Lynne L. Butler
language : it
Publisher:
Release Date : 1994

Subgroup Lattices And Symmetric Functions written by Lynne L. Butler and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with categories.

The Fundamental Lemma For The Shalika Subgroup Of Gl 4

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Author : Solomon Friedberg
language : en
Publisher: American Mathematical Soc.
Release Date : 1996

The Fundamental Lemma For The Shalika Subgroup Of Gl 4 written by Solomon Friedberg and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.

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.

The Major Counting Of Nonintersecting Lattice Paths And Generating Functions For Tableaux

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Author : Christian Krattenthaler
language : en
Publisher: American Mathematical Soc.
Release Date : 1995

The Major Counting Of Nonintersecting Lattice Paths And Generating Functions For Tableaux written by Christian Krattenthaler and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.

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.

M Bius Functions Incidence Algebras And Power Series Representations

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Author : Arne Dür
language : en
Publisher: Springer
Release Date : 2006-11-14

M Bius Functions Incidence Algebras And Power Series Representations written by Arne Dür and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

Handbook Of Enumerative Combinatorics

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Author : Miklos Bona
language : en
Publisher: CRC Press
Release Date : 2015-03-24

Handbook Of Enumerative Combinatorics written by Miklos Bona and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-24 with Mathematics categories.

Presenting the state of the art, the Handbook of Enumerative Combinatorics brings together the work of today's most prominent researchers. The contributors survey the methods of combinatorial enumeration along with the most frequent applications of these methods.This important new work is edited by Miklos Bona of the University of Florida where he

Surveys In Combinatorics 2003

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Author : C. D. Wensley
language : en
Publisher: Cambridge University Press
Release Date : 2003-07-24

Surveys In Combinatorics 2003 written by C. D. Wensley and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-24 with Mathematics categories.

The British Combinatorial Conference is held every two years and is a key event for mathematicians worldwide working in combinatorics. In June 2003 the conference was held at the University of Wales, Bangor. The papers contained here are surveys contributed by the invited speakers and are of the high quality that befits the event. There is also a tribute to Bill Tutte who had a long-standing association with the BCC. The papers cover topics currently attracting significant research interest as well as some less traditional areas such as the combinatorics of protecting digital content. They will form an excellent resource for established researchers as well as graduate students who will find much here to inspire future work.

Bounded Littlewood Identities

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Author : Eric M. Rains
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-07-21

Bounded Littlewood Identities written by Eric M. Rains and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-21 with Education categories.

We describe a method, based on the theory of Macdonald–Koornwinder polynomials, for proving bounded Littlewood identities. Our approach provides an alternative to Macdonald’s partial fraction technique and results in the first examples of bounded Littlewood identities for Macdonald polynomials. These identities, which take the form of decomposition formulas for Macdonald polynomials of type (R, S) in terms of ordinary Macdonald polynomials, are q, t-analogues of known branching formulas for characters of the symplectic, orthogonal and special orthogonal groups. In the classical limit, our method implies that MacMahon’s famous ex-conjecture for the generating function of symmetric plane partitions in a box follows from the identification of GL(n, R), O(n) as a Gelfand pair. As further applications, we obtain combinatorial formulas for characters of affine Lie algebras; Rogers–Ramanujan identities for affine Lie algebras, complementing recent results of Griffin et al.; and quadratic transformation formulas for Kaneko–Macdonald-type basic hypergeometric series.

Textile Systems For Endomorphisms And Automorphisms Of The Shift

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Author : Masakazu Nasu
language : en
Publisher: American Mathematical Soc.
Release Date : 1995

Textile Systems For Endomorphisms And Automorphisms Of The Shift written by Masakazu Nasu and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.

We introduce the notion of a textile system. Using this, we study the dynamical properties of endomorphisms and automorphisms of topological Markov shifts including one-sided ones. The dynamical properties of automorphisms of sofic systems are also studied.