no. 4
Combinatoire, Théorie des probabilités
Dual Grothendieck polynomials via last-passage percolation
[Polynômes de Grothendieck duales par percolation de dernier passage]
Yeliussizov, Damir1
1 Kazakh-British Technical University, 59 Tole bi st, Almaty 050000, Kazakhstan
Comptes Rendus. Mathématique, Tome 358 (2020) no. 4, pp. 497-503.

L’anneau de fonctions symétriques a une base de polynômes de Grothendieck duales qui sont des déformations K-théoriques non homogénes des polynômes de Schur. Nous prouvons que les polynômes de Grothendieck duales déterminent distributions des colonnes pour un modèle de percolation dirigée de dernier passage.

The ring of symmetric functions has a basis of dual Grothendieck polynomials that are inhomogeneous K-theoretic deformations of Schur polynomials. We prove that dual Grothendieck polynomials determine column distributions for a directed last-passage percolation model.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.67
Classification : 05E05, 60K35, 60C05
Yeliussizov, Damir 1

1 Kazakh-British Technical University, 59 Tole bi st, Almaty 050000, Kazakhstan 
@article{CRMATH_2020__358_4_497_0,
     author = {Yeliussizov, Damir},
     title = {Dual {Grothendieck} polynomials via last-passage percolation},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {497--503},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {4},
     year = {2020},
     doi = {10.5802/crmath.67},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/crmath.67/}
}
TY  - JOUR
AU  - Yeliussizov, Damir
TI  - Dual Grothendieck polynomials via last-passage percolation
JO  - Comptes Rendus. Mathématique
PY  - 2020
SP  - 497
EP  - 503
VL  - 358
IS  - 4
PB  - Académie des sciences, Paris
UR  - http://www.numdam.org/articles/10.5802/crmath.67/
DO  - 10.5802/crmath.67
LA  - en
ID  - CRMATH_2020__358_4_497_0
ER  - 
%0 Journal Article
%A Yeliussizov, Damir
%T Dual Grothendieck polynomials via last-passage percolation
%J Comptes Rendus. Mathématique
%D 2020
%P 497-503
%V 358
%N 4
%I Académie des sciences, Paris
%U http://www.numdam.org/articles/10.5802/crmath.67/
%R 10.5802/crmath.67
%G en
%F CRMATH_2020__358_4_497_0
Yeliussizov, Damir. Dual Grothendieck polynomials via last-passage percolation. Comptes Rendus. Mathématique, Tome 358 (2020) no. 4, pp. 497-503. doi : 10.5802/crmath.67. http://www.numdam.org/articles/10.5802/crmath.67/

[1] Baryshnikov, Yuliy GUEs and queues, Probab. Theory Relat. Fields, Volume 119 (2001) no. 2, pp. 256-274 | DOI | MR | Zbl

[2] Borodin, Alexei; Okounkov, Andrei A Fredholm determinant formula for Toeplitz determinants, Integral Equations Oper. Theory, Volume 37 (2000) no. 4, pp. 386-396 | DOI | MR | Zbl

[3] Buch, Anders S. A Littlewood–Richardson rule for the K-theory of Grassmannians, Acta Math., Volume 189 (2002) no. 1, pp. 37-78 | DOI | MR | Zbl

[4] Johansson, Kurt Shape fluctuations and random matrices, Commun. Math. Phys., Volume 209 (2000) no. 2, pp. 437-476 | DOI | MR | Zbl

[5] Johansson, Kurt Discrete orthogonal polynomial ensembles and the Plancherel measure, Ann. Math., Volume 153 (2001) no. 1, pp. 259-296 | DOI | MR | Zbl

[6] Johansson, Kurt Random growth and random matrices, 3rd European congress of mathematics (ECM) (Progress in Mathematics), Volume 201, Birkhäuser, 2001, pp. 445-456 | DOI | MR | Zbl

[7] Lam, Thomas; Pylyavskyy, Pavlo Combinatorial Hopf algebras and K-homology of Grassmannians, Int. Math. Res. Not., Volume 2007 (2007) no. 24, rnm125, 48 pages | MR | Zbl

[8] Lenart, Cristian Combinatorial aspects of the K-theory of Grassmannians, Ann. Comb., Volume 4 (2000) no. 1, pp. 67-82 | DOI | MR | Zbl

[9] Okounkov, Andrei; Reshetikhin, Nikolai Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram, J. Am. Math. Soc., Volume 16 (2003) no. 3, pp. 581-603 | DOI | MR | Zbl

[10] Romik, Dan The surprising mathematics of longest increasing subsequences, Institute of Mathematical Statistics Textbooks, 4, Cambridge University Press, 2015 | MR | Zbl

[11] Seppäläinen, Timo Lecture notes on the corner growth model (2009) (unpublished notes, available at https://www.researchgate.net/publication/228814673_Lecture_Notes_on_the_Corner_Growth_Model)

[12] Tracy, Craig A.; Widom, Harold On the distributions of the lengths of the longest monotone subsequences in random words, Probab. Theory Relat. Fields, Volume 119 (2001) no. 3, pp. 350-380 | DOI | MR | Zbl

[13] Yeliussizov, Damir Duality and deformations of stable Grothendieck polynomials, J. Algebr. Comb., Volume 45 (2017) no. 1, pp. 295-344 | DOI | MR | Zbl

[14] Yeliussizov, Damir Enumeration of plane partitions by descents (2019) (https://arxiv.org/abs/1911.03259)

[15] Yeliussizov, Damir Random plane partitions and corner distributions (2019) (https://arxiv.org/abs/1910.13378)

[16] Yeliussizov, Damir Symmetric Grothendieck polynomials, skew Cauchy identities, and dual filtered Young graphs, J. Comb. Theory, Ser. A, Volume 161 (2019), pp. 453-485 | DOI | MR | Zbl

[17] Yeliussizov, Damir Positive specializations of symmetric Grothendieck polynomials, Adv. Math., Volume 363 (2020), 107000, 35 pages | MR | Zbl

Cité par Sources :