Subgroup Lattices and Symmetric Functions
1994
American Mathematical Society (Verlag)
9780821826003 (ISBN)
American Mathematical Society (Verlag)
9780821826003 (ISBN)
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Presents foundational research on two approaches to studying subgroup lattices of finite abelian $p$-groups. This book offers a combinatorial interpretation of the Betti polynomials of the Cohen-Macaulay posets.
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.
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.
Introduction Subgroups of finite Abelian groups Hall-Littlewood symmetric functions Some enumerative combinatorics Some algebraic combinatorics.
| Erscheint lt. Verlag | 1.6.1995 |
|---|---|
| Reihe/Serie | Memoirs of the American Mathematical Society |
| Zusatzinfo | illustrations |
| Verlagsort | Providence |
| Sprache | englisch |
| Gewicht | 305 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre | |
| ISBN-13 | 9780821826003 / 9780821826003 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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