Group actions on Stanley-Reisner rings and invariants of permutation groups☆
Adriano M. Garsia,Dennis Stanton +1 more
TLDR
In this paper, a combinatorial method for the construction of free bases for the symmetric polynomials over the subset lattice has been proposed, where the action of a symmetric group on the Stanley-Reisner ring is studied.About:
This article is published in Advances in Mathematics.The article was published on 1984-02-01 and is currently open access. It has received 129 citations till now. The article focuses on the topics: Group ring & Symmetric group.read more
Citations
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f-vectors and h-vectors of simplicial posets
TL;DR: Stanely et al. as mentioned in this paper gave a complete characterization of the f-vectors of simplicial posets and of Cohen-Macaulay simplicial pose&, and an almost complete characterization for Gorenstein simplicial polynomials.
Book ChapterDOI
Combinatorics of the Free Lie Algebra and the Symmetric Group
TL;DR: In this paper, the authors show that a number of classical results concerning the Free Lie Algebra are intimately related to and may be derived from the study of certain permutation statistics, and systematically explore this connection by developing the whole theory from the combinatorial point of view.
Journal Article
The Tutte polynomial of a graph, depth-first search, and simplicial complex partitions.
Ira M. Gessel,Bruce E. Sagan +1 more
TL;DR: In this paper, the authors show that by partitioning certain simplicial complexes related to a graph G into intervals, one can provide combinatorial demonstrations of these results, e.g., subgraphs, spanning trees, acyclic orientations, inversions and parking functions.
Journal ArticleDOI
The Tutte Polynomial of a Graph, Depth-first Search
Ira M. Gessel,Bruce E. Sagan +1 more
TL;DR: It is shown that by partitioning certain simplicial complexes related to G into intervals, one can provide combinatorial demonstrations of the two-variable Tutte polynomial results.
References
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Book
Introduction to Lie Algebras and Representation Theory
TL;DR: In this paper, Semisimple Lie Algebras and root systems are used for representation theory, isomorphism and conjugacy theorem, and existence theorem for representation.
Book
Groupes et algèbres de Lie
TL;DR: Les Elements de mathematique de Nicolas Bourbaki ont pour objet une presentation rigoureuse, systematique et sans prerequis des mathematiques depuis leurs fondements as mentioned in this paper.
Book
Simple groups of Lie type
TL;DR: In this article, the authors present a generalization of the Weyl Group to the Chevalley Group, and further properties of the twisted simple groups, including generators, relations and automorphisms.