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Author Butler, Lynne M., 1955-

Title Subgroup lattices and symmetric functions / Lynne M. Butler
Published Providence, RI : American Mathematical Society, ©1994
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Description 1 online resource (vi, 160 pages) : illustrations
Series Memoirs of the American Mathematical Society, 1947-6221 ; v. 539
Memoirs of the American Mathematical Society ; no. 539. 0065-9266
Contents 1. Subgroups of finite Abelian groups 2. Hall-Littlewood symmetric functions
Summary This work presents foundational research on two approaches to studying subgroup lattices of finite abelian [italic]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. We complete Lascoux and Schützenberger's proof that Kostka polynomials are nonnegative, and discuss their monotonicity results and a conjecture on Macdonald's two-variable Kostka functions
Notes "November 1994, volume 112."
Bibliography Includes bibliographical references (pages 157-160)
Notes Print version record
Subject Finite groups.
Lattice theory.
Symmetric functions.
Eindige groepen.
31.00 mathematics: general.
31.21 theory of groups.
Endliche Gruppe
Finite groups.
Lattice theory.
MATHEMATICS -- Pre-Calculus.
MATHEMATICS -- Reference.
Symmetric functions.
Symmetrische Funktion
Teoria Dos Grupos.
Verband Mathematik
Form Electronic book
Author American Mathematical Society.
ISBN 1470401185