Hostname: page-component-848d4c4894-ndmmz Total loading time: 0 Render date: 2024-05-21T07:55:10.190Z Has data issue: false hasContentIssue false
  • English
  • Français

Some Results on Two Conjectures of Schützenberger

Published online by Cambridge University Press:  20 November 2018

Marc Desgroseilliers ,
Benoit Larose ,
Claudia Malvenuto  and
Christelle Vincent
Marc Desgroseilliers
Affiliation:
Department of Mathematics and Statistics, McGill University, Burnside Hall room 1005, 805 Sherbrooke West, Montréal, Qc, Canada, H3A 2K6 e-mail: marc.desgroseilliers2@mail.mcgill.ca
Benoit Larose
Affiliation:
Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve West, Montréal, Qc, Canada, H3G 1M8 e-mail: larose@mathstat.concordia.ca
Claudia Malvenuto
Affiliation:
Dipartimento di Informatica, Università degli Studi “La Sapienza”, Via Salaria, 113, I–00198, Roma – Italy e-mail: claudia@di.uniroma1.it
Christelle Vincent
Affiliation:
Mathematics Department, University of Wisconsin-Madison, 480 Lincoln Drive, Madison WI 53706-1388 e-mail: vincent@math.wisc.edu
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.

Keywords

05E1005A99Evacuation of Standard Young tableaux
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 53 , Issue 3 , 01 September 2010 , pp. 453 - 465
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. 121–135.Google Scholar
[2] Gansner, E. R., On the equality of two plane partition correspondences. Discrete Math. 30(1980), no. 2, 121–132. 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, 79–113. 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, 137–143. 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, 103–112. 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), 117–128.Google Scholar
[9] Schützenberger, M.-P., Promotion des morphismes d’ensembles ordonnés. Discrete Math. 2(1972), 73–94. 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. 59–113.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. 257–264.Google Scholar