Journal of Algebraic Combinatorics
, Volume 4, Issue 1, pp 545
First online:
Schensted Algorithms for Dual Graded Graphs
 Sergey FominAffiliated withDepartment of Mathematics, Massachusetts Institute of TechnologyTheory of Algorithms Laboratory, SPIIRAN, Russian Academy of Sciences
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This paper is a sequel to [3]. We keep the notation and terminology and extend the numbering of sections, propositions, and formulae of [3].
The main result of this paper is a generalization of the RobinsonSchensted correspondence to the class of dual graded graphs introduced in [3], This class extends the class of Ygraphs, or differential posets [22], for which a generalized Schensted correspondence was constructed earlier in [2].
The main construction leads to unified bijective proofs of various identities related to path counting, including those obtained in [3]. It is also applied to permutation enumeration, including rook placements on Ferrers boards and enumeration of involutions.
As particular cases of the general construction, we rederive the classical algorithm of Robinson, Schensted, and Knuth [19, 12], the SaganStanley [18], SaganWorley [16, 29] and Haiman's [11] algorithms and the author's algorithm for the YoungFibonacci graph [2]. Some new applications are suggested.
The rim hook correspondence of Stanton and White [23] and Viennot's bijection [28] are also special cases of the general construction of this paper.
In [5], the results of this paper and the previous paper [3] were presented in a form of extended abstract.
 Title
 Schensted Algorithms for Dual Graded Graphs
 Journal

Journal of Algebraic Combinatorics
Volume 4, Issue 1 , pp 545
 Cover Date
 199501
 DOI
 10.1023/A:1022404807578
 Print ISSN
 09259899
 Online ISSN
 15729192
 Publisher
 Kluwer Academic PublishersPlenum Publishers
 Additional Links
 Topics
 Keywords

 discrete algorithm
 enumerative combinatorics
 poset
 Young diagram
 Authors

 Sergey Fomin ^{(1)} ^{(2)}
 Author Affiliations

 1. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, 021394307
 2. Theory of Algorithms Laboratory, SPIIRAN, Russian Academy of Sciences, Russia