CIRM - Videos & books Library - Le diamant aztèque

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Authors : Corteel, Sylvie (Author of the conference)
CIRM (Publisher )

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Abstract : Le but du mini-cours sera de faire un cours introductif à différentes méthodes énumeratives à travers l'exemple des pavages par dominos du diamant aztèque. On essaiera de voir les fonctions (super)-symétriques, les moments de polynômes bi-orthogonaux, les évaluations de determinants, les algorithmes de génération...

MSC Codes :
05A15 - Exact enumeration problems, generating functions
33C45 - Orthogonal polynomials and functions (Chebyshev, Legendre, Gegenbauer, Jacobi, Laguerre, Hermite, Hahn, etc.)

Information on the Video

Film maker :

Hennenfent, Guillaume

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https://videos.cirm-math.fr/2015-03-16_Corteel_part1.mp4

Information on the Event

Event Title : ALEA Days / Journées Aléa
Event Organizers : Bettinelli, Jérémie ; Chassaing, Philippe ; Mishna, Marni ; Viola, Alfredo
Dates : 16/03/15 - 20/03/15
Event Year : 2015
Event URL : http://alea15.math.cnrs.fr/

Citation Data

DOI : 10.24350/CIRM.V.18737103
Cite this video as: Corteel, Sylvie (2015). Le diamant aztèque - Cours 1. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18737103
URI : http://dx.doi.org/10.24350/CIRM.V.18737103

Bibliography

[1] Baryshnikov, Y., & Pemantle, R. (2011). Asymptotics of multivariate sequences, part III: quadratic points. Advances in Mathematics, 228(6), 3127-3206 - http://dx.doi.org/10.1016/j.aim.2011.08.004

[2] Bouttier, J., Chapuy, G., & Corteel, S. (2014). From Aztec diamonds to pyramids: steep tilings. - http://arxiv.org/abs/1407.0665v2

[3] Chhita, S., & Young, B. (2014). Coupling functions for domino tilings of Aztec diamond. Advances in Mathematics, 259, 173-251 - http://dx.doi.org/10.1016/j.aim.2014.01.023

[4] Cohn, H., Elkies, N., & Propp, J. (1996). Local statistics for random domino tilings of the Aztec diamond. Duke Mathematical Journal, 85(1), 117-166 - http://dx.doi.org/10.1215/s0012-7094-96-08506-3

[5] Du, P., Gessel, I., lonescu, A., & Propp, J. The Aztec Diamond Edge-Probability generating function, preprint -

[6] Elkies, N., Kuperberg, G., Larsen, M., & Propp, J. (1992). Alternating-sign matrices and domino tilings. I. Journal of Algebraic Combinatorics, 1(2), 111-132 - http://dx.doi.org/10.1023/A:1022420103267

[7] Elkies, N., Kuperberg, G., Larsen, M., & Propp, J. (1992). Alternating-sign matrices and domino tilings. II. J. Algebraic Combin. 1(3), 219-234 - http://dx.doi.org/10.1023/A:1022483817303

[8] Fleming, B.J., & Forrester, Peter J. (2011). Interlaced particle systems and tilings ofthe Aztec diamond. Journal of Statistical Physics, 142(3), 441-459 - http://dx.doi.org/10.1007/s10955-011-0121-2

[9] Johansson, K. (2005). The arctic circle boundary and the Airy process. The Annals of Probability, 33(1), 1-30 - http://dx.doi.org/10.1214/009117904000000937

[10] Kamioka, S. (2014). Laurent biorthogonal polynomials, q-Narayana polynomials and domino tilings of the Aztec diamonds. Journal of Combinatorial Theory, Series A, 123(1), 14-29 - http://dx.doi.org/10.1016/j.jcta.2013.11.002

[11] Nordenstam, E. (2010). On the shuffling algorithm for domino tilings. Electronic Journal of Probability, 15(3), 75-95 - http://dx.doi.org/10.1214/ejp.v15-730

[12] Pemantle, R., & Wilson, M.C. (2013). Analytic combinatorics in several variables. Cambridge: Cambridge University Press. (Cambridge Studies in Advanced Mathematics, 140) - http://dx.doi.org/10.1017/CBO9781139381864

[13] Propp, J. (2003). Generalized domino-shuffling. Theoretical Computer Science, 303(2-3), 267-301 - http://dx.doi.org/10.1016/s0304-3975(02)00815-0

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