Some combinatorics of rhomboid-shaped fully packed loop configurations

Abstract : The study of rhomboid-shaped fully packed loop configurations (RFPLs) is inspired by the work of Fischer and Nadeau on triangular fully packed loop configurations (TFPLs). By using the same techniques as they did some nice combinatorics for RFPLs arise. To each RFPL and to each oriented RFPL a quadruple of binary words (α ,β ;γ ,δ ) – its so-called boundary – is assigned. There are necessary conditions for the boundary of an RFPL respectively an oriented RFPL. For instance, it has to fulfill the inequality $d(γ )+d(δ )\geq(α )+d(β )+\vert α \vert _0\vert β \vert _1$, where $\vert α \vert _i $ denotes the number of occurrences of $i=0,1$ in α and d(α ) denotes the number of inversions of α . Furthermore, the number of ordinary RFPLs with boundary (α ,β ;γ ,δ ) can be expressed in terms of oriented RFPLs with the same boundary. Finally, oriented RFPLs with boundary (α ,β ;γ ,δ ) such that $d(γ )+d(δ )=d(α )+d(β )+\vert α \vert _0\vert β \vert _1$ are considered. They are in bijection with rhomboid-shaped Knutson-Tao puzzles. Also, Littlewood-Richardson tableaux of defect d are defined. They can be understood as a generalization of Littlewood-Richardson tableaux. Those tableaux are in bijection with rhomboid-shaped Knutson-Tao puzzles.
Type de document :
Communication dans un congrès
Louis J. Billera and Isabella Novik. 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), 2014, Chicago, United States. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), pp.765-776, 2014, DMTCS Proceedings
Liste complète des métadonnées

Littérature citée [9 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/hal-01207566
Contributeur : Coordination Episciences Iam <>
Soumis le : jeudi 1 octobre 2015 - 09:28:31
Dernière modification le : mardi 7 mars 2017 - 15:25:42
Document(s) archivé(s) le : samedi 2 janvier 2016 - 10:48:52

Fichier

dmAT0166.pdf
Fichiers éditeurs autorisés sur une archive ouverte

Identifiants

  • HAL Id : hal-01207566, version 1

Collections

Citation

Sabine Beil. Some combinatorics of rhomboid-shaped fully packed loop configurations. Louis J. Billera and Isabella Novik. 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), 2014, Chicago, United States. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), pp.765-776, 2014, DMTCS Proceedings. 〈hal-01207566〉

Partager

Métriques

Consultations de la notice

50

Téléchargements de fichiers

57