منابع مشابه
Indecomposable Summands of Foulkes Modules
In this paper we study the modular structure of the permutation module H ) of the symmetric group S2n acting on set partitions of a set of size 2n into n sets each of size 2, defined over a field of odd characteristic p. In particular we characterize the vertices of the indecomposable summands of H ) and fully describe all of its indecomposable summands that lie in blocks of p-weight at most tw...
متن کاملSome Computations Regarding Foulkes' Conjecture
We describe how certain permutation actions of large symmetric groups can be efficiently implemented on a computer. Using a specially tailored adaptation of a general technique to enumerate huge orbits, and substantial distributed computation on a cluster of workstations, we collect further evidence related to the approach to Foulkes’ conjecture suggested in [Black and List, 1989]. 1 Foulkes’ c...
متن کاملSet Families and Foulkes Modules
We construct a new family of homomorphisms from Specht modules into Foulkes modules for the symmetric group. These homomorphisms are used to give a combinatorial description of the minimal partitions (in the dominance order) which label the irreducible characters appearing as summands of the characters of Foulkes modules. The homomorphisms are defined using certain families of subsets of the na...
متن کاملSome Plethystic Identities And Kostka-Foulkes Polynomials
plays an important role in the Garsia-Haglund proof of the q, t-Catalan conjecture, [2]. Let ΛQ(q,t) be the space of symmetric functions of degree n, over the field of rational functions Q(q, t), and let ∇ : ΛQ(q,t) → Λ n Q(q,t) be the Garsia-Bergeron operator. By studying recursions, Garsia and Haglund show that the coefficient of the elementary symmetric function en(X) in the image ∇(En,k(X))...
متن کاملA Generalization of the Kostka-foulkes Polynomials
Combinatorial objects called rigged configurations give rise to q-analogues of certain Littlewood-Richardson coefficients. The Kostka-Foulkes polynomials and twocolumn Macdonald-Kostka polynomials occur as special cases. Conjecturally these polynomials coincide with the Poincaré polynomials of isotypic components of certain graded GL(n)-modules supported in a nilpotent conjugacy class closure i...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1980
ISSN: 0012-365X
DOI: 10.1016/0012-365x(80)90060-6