Subgroup Lattices and Symmetric Functions.

Intro -- Contents -- Introduction -- 1 Subgroups of Finite Abelian Groups -- 1.1 Methods and Results -- 1.2 The case λ = 1[sup(n)]: Chains and Invariants -- 1.3 Motivation: Subgroups and Tabloids -- 1.4 The case λ ≠ 1[sup(n)]: Chains -- 1.5 The case λ ≠ 1[sup(n)]: Invariants -- 1.6 Birkhoff's standard matrices -- 1.7 A more natural alternative -- Table 1 -- 2 Hall-Littlewood Symmetric Functions -- 2.1 Introduction -- 2.2 Littlewood's expression for Pλ(x -- q) -- 2.3 Robinson-Schensted insertion and Jeu de Taquin -- 2.4 Charge -- 2.5 Nonnegativity of Kostka polynomials -- 2.6 Monotonicity of Kostka polynomials -- 2.7 Two variable Kostka functions -- Table 2 -- A Some enumerative combinatorics -- A.1 Partitions and finite abelian groups -- B Some algebraic combinatorics -- B.1 Symmetric functions -- B.2 Tableau terminology.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.