Subgroup lattices and symmetric functions
著者
書誌事項
Subgroup lattices and symmetric functions
（Memoirs of the American Mathematical Society, no. 539）
American Mathematical Society, 1994
大学図書館所蔵 全20件
注記
"November 1994, volume 112, number 539 (third of 4 numbers)"--T.p
Includes bibliography (p. 157-160)
内容説明・目次
内容説明
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.
目次
Introduction Subgroups of finite Abelian groups Hall-Littlewood symmetric functions Some enumerative combinatorics Some algebraic combinatorics.
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