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 件 / 全20件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
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.
「Nielsen BookData」 より