Abstract
We study four operations defined on pairs of tableaux. Algorithms for the first three involve the familiar procedures of jeu de taquin, row insertion, and column insertion, respectively. The fourth operation of hopscotch is new, although specialised versions have appeared previously. Like the other three operations, hopscotch may be computed with a set of local rules in a growth diagram, and it preserves Knuth equivalence class. Each of these four operations gives rise to an a priori distinct theory of dual equivalence. We show that these four theories coincide. The four operations are linked via the involutive tableau operations of complementation and conjugation.
Résumé
Nous étudions quatre opérations définies sur les paires de tableaux de Young. Les algorithmes pour trois des opérations impliquent les procédures familières de jeu de taquin, l’insertion par rangs, et l’insertion par colonnes, respectivement. La quatrième opération de hopscotch est nouvelle, bien que les versions spécialisiés aient apparu précédemment. Comme les trois autres opérations, hopscotch peut être calculée avec une série de règles locales dans un diagramme de croissance, et elle conserve la classe d’équivalence de Knuth. Chacune de ces quatre opérations engendre un théorie a priori distincte d’équivalence duale. Nous montrons que ces quatre théories coïncident. Les quatre opérations sont reliées par les opérations involutives de complémentation et de conjugaison.
Supported in part by NSERC grant OGP0170279 and NSF grant DMS-9701755
Supported in part by NSERC grant OGP0105492
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Roby, T., Sottile, F., Stroomer, J., West, J. (2000). Jeux de tableaux. In: Krob, D., Mikhalev, A.A., Mikhalev, A.V. (eds) Formal Power Series and Algebraic Combinatorics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04166-6_30
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DOI: https://doi.org/10.1007/978-3-662-04166-6_30
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