A Model for the Double Cosets of Young Subgroups
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چکیده
There are several results concerning double cosets of Young subgroups of symmetric groups which are often proved as corollaries of more general results about Coxeter groups. In this note we give a selection of these results and give them short combinatorial proofs. The replacement for the machinery of Coxeter groups consists of some simple combinatorial arguments involving tableaux. Inevitably we must repeat a few definitions from and standard lemmas from Coxeter theory, but I have tried to keep this to a minimum. The idea behind this approach is well known to experts (see for instance [1] and [2, Ch. 13]), but I have not yet seen a really explicit account of it. (The introduction of ‘labelled’ tableaux in Remark 3.2 may be new.)
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A Model for the Double Cosets of Young Subgroups
There are several results concerning double cosets of Young subgroups of symmetric groups which are often proved as corollaries of more general results about Coxeter groups. In this note we give a selection of these results and give them the short combinatorial proofs they deserve. Our replacement for the machinery of Coxeter groups consists of some simple combinatorial arguments involving tabl...
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