Geodesic
Set families and Foulkes modules
Journal of Algebraic Combinatorics, Tome 34 (2011) no. 3, pp. 525-544.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 natural numbers. These families are of independent interest; we prove a number of combinatorial results concerning them.
Keywords: keywords foulkes' conjecture, Specht module, foulkes module, module homomorphism, closed set family 
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     author = {Paget, Rowena and Wildon, Mark},
     title = {Set families and {Foulkes} modules},
     journal = {Journal of Algebraic Combinatorics},
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     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2011__34_3_a0/}
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Paget, Rowena; Wildon, Mark. Set families and Foulkes modules. Journal of Algebraic Combinatorics, Tome 34 (2011) no. 3, pp. 525-544. http://geodesic.mathdoc.fr/item/JAC_2011__34_3_a0/