Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-12-01T06:25:24.631Z Has data issue: false hasContentIssue false

Some Results on Two Conjectures of Schützenberger

Published online by Cambridge University Press:  20 November 2018

Marc Desgroseilliers
Affiliation:
Department of Mathematics and Statistics, McGill University, Burnside Hall room 1005, 805 Sherbrooke West, Montréal, Qc, Canada, H3A 2K6 e-mail: [email protected]
Benoit Larose
Affiliation:
Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve West, Montréal, Qc, Canada, H3G 1M8 e-mail: [email protected]
Claudia Malvenuto
Affiliation:
Dipartimento di Informatica, Università degli Studi “La Sapienza”, Via Salaria, 113, I–00198, Roma – Italy e-mail: [email protected]
Christelle Vincent
Affiliation:
Mathematics Department, University of Wisconsin-Madison, 480 Lincoln Drive, Madison WI 53706-1388 e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We present some partial results concerning two conjectures of Schützenberger on evacuations of Young tableaux.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2010

References

[1] Foata, D., Une propriété de vidage-remplissage des tableaux de Young. In: Combinatoire et représentation du groupe symétrique, Lecture Notes in Math. 579, Springer, Berlin, 1977, pp. 121135.Google Scholar
[2] Gansner, E. R., On the equality of two plane partition correspondences. Discrete Math. 30(1980), no. 2, 121132. doi:10.1016/0012-365X(80)90114-4Google Scholar
[3] Haiman, M. D., Dual equivalence with applications, including a conjecture of Proctor. Discrete Math. 99(1999), no. 1–3, 79113. doi:10.1016/0012-365X(92)90368-PGoogle Scholar
[4] Knuth, D. E, The art of computer programming: Sorting and searching. Vol. 3. Second ed., Addison-Wesley, Reading, MA, 1988.Google Scholar
[5] Malvenuto, C. and Reutenauer, C., Evacuation of labelled graphs. Discrete Math. 132(1994), no. 1–3, 137143. doi:10.1016/0012-365X(92)00569-DGoogle Scholar
[6] Reifegerste, A., Permutation sign under the Robinson–Schensted correspondence. Ann. Comb. 8(2004), no. 1, 103112. doi:10.1007/s00026-004-0208-4Google Scholar
[7] Sagan, B. E., The symmetric group: representations, combinatorial algorithms and symmetric functions. Wadsworth and Brooks/Cole Mathematics Series.Wadsworth and Brooks/Cole Advanced Books and Software, Pacific Grove, CA, 1991.Google Scholar
[8] Schützenberger, M.-P., Quelques remarques sur une construction de Schensted. Math. Scand. 12(1963), 117128.Google Scholar
[9] Schützenberger, M.-P., Promotion des morphismes d’ensembles ordonnés. Discrete Math. 2(1972), 7394. doi:10.1016/0012-365X(72)90062-3Google Scholar
[10] Schützenberger, M.-P., La correspondance de Robinson. In: Combinatoire et représentation du groupe symétrique, Lecture Notes in Math. 579, Springer, Berlin, 1976, pp. 59113.Google Scholar
[11] Schützenberger, M.-P., Evacuations. In: Colloquio Internazionale sulle Teorie Combinatorie (Roma, 1973), Atti dei Convegni Lincei 17, Accad. Naz. Lincei, Rome, 1976, pp. 257264.Google Scholar