Four correspondences between graphs and generalized young tableaux

Burge, William H.

doi:10.1016/0097-3165(74)90024-7

Cited by 83 publications

(84 citation statements)

References 6 publications

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“…For each box, we pick a connected triplet on southwest, northwest and southeast corners. That is, suppose the box has index (m, k) we fix arbitrary p 1 , p 2 and p 3 …”

Section: Theorem 3 For Any Permutation σ ∈ S N and Standard Tableau Pmentioning

confidence: 99%

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A symmetry property for $$q$$ q -weighted Robinson–Schensted and other branching insertion algorithms

Pei

2014

J Algebr Comb

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In [19], a q-weighted version of the Robinson-Schensted algorithm was introduced. In this paper, we show that this algorithm has a symmetry property analogous to the well-known symmetry property of the usual Robinson-Schensted algorithm. The proof uses a generalisation of the growth diagram approach introduced by Fomin [5][6][7][8]. This approach, which uses 'growth graphs', can also be applied to a wider class of insertion algorithms which have a branching structure, including some of the other q-weighted versions of the Robinson-Schensted algorithm which have recently been introduced by .

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“…For each box, we pick a connected triplet on southwest, northwest and southeast corners. That is, suppose the box has index (m, k) we fix arbitrary p 1 , p 2 and p 3 …”

Section: Theorem 3 For Any Permutation σ ∈ S N and Standard Tableau Pmentioning

confidence: 99%

“…Note that the matrix becomes the permutation matrix when the RSK algorithm is restricted to permutation, and hence the transposition of the matrix corresponds to inversion of the permutation. Burge gives a similar generalisation of the column insertion algorithm [3], which we refer to as Burge's algorithm.…”

Section: Introductionmentioning

confidence: 99%

A symmetry property for $$q$$ q -weighted Robinson–Schensted and other branching insertion algorithms

Pei

2014

J Algebr Comb

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“…A combinatorial proof of the Littlewood identities (3.3) and (4.1) involving matchings is given by Burge [17]. Macdonald [35,I 5 Ex.…”

Section: Hopf Trace Formula and Littlewood's Identitymentioning

confidence: 99%

Topology of matching, chessboard, and general bounded degree graph complexes

Wachs

2003

Algebra Universalis

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Abstract. We survey results and techniques in the topological study of simplicial complexes of (di-, multi-, hyper-)graphs whose node degrees are bounded from above. These complexes have arisen is a variety of contexts in the literature. The most wellknown examples are the matching complex and the chessboard complex. The topics covered here include computation of Betti numbers, representations of the symmetric group on rational homology, torsion in integral homology, homotopy properties, and connections with other fields.

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“…Let ϕ denote the Burge correspondence [9] (see also [12, A4.1]). Numerically, it defines a one-to-one map between the same sets as the RSK map ϕ :…”

Section: Burge Correspondencementioning

confidence: 99%