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    3. Subgroup Lattices and Symmetric Functions

    Subgroup Lattices and Symmetric Functions

    Posted By: DZ123
    Date: 7 Apr 2016 15:59:13
    Subgroup Lattices and Symmetric Functions

    Lynne M. Butler, "Subgroup Lattices and Symmetric Functions"
    English | 1994 | ISBN: 082182600X | PDF | pages: 166 | 6,4 mb

    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 Schutzenberger's proof that Kostka polynomials are nonnegative, then discusses their monotonicity result and a conjecture on Macdonald's two-variable Kostka functions.

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