Jack polynomials and free cumulants

Michel Lassalle

Type: Article

Publication Date: 2009-08-16

Citations: 51

DOI: https://doi.org/10.1016/j.aim.2009.07.007

View Publication

Download PDF

Locations

Advances in Mathematics - View
arXiv (Cornell University) - View - PDF
HAL (Le Centre pour la Communication Scientifique Directe) - View
DataCite API - View

Similar Works

Action	Title	Year	Authors
+	Free probability and representations of large symmetric groups	2003	Piotr Śniady
+ PDF Chat	A Spin Analogue of Kerov Polynomials	2018	Sho Matsumoto
+	Structure coefficients for Jack characters: approximate factorization property	2016	Piotr Śniady
+	Zonal polynomials via Stanley-F\'eray formula and free cumulants	2010	Valentin Féray Piotr Śniady
+	On Kerov polynomials for Jack characters	2012	Maciej Dołęga Valentin Féray
+	Zonal polynomials via Stanleyʼs coordinates and free cumulants	2011	Valentin Féray Piotr Śniady
+ PDF Chat	On Kerov polynomials for Jack characters (extended abstract)	2013	Valentin Féray Maciej Dołęga
+ PDF Chat	Gaussian fluctuations of Young diagrams and structure constants of Jack characters	2016	Maciej Dołęga Valentin Féray
+	Jack polynomials and orientability generating series of maps	2013	Maciej Dołęga Valentin Féray Piotr Śniady
+	Jack polynomials and orientability generating series of maps	2013	Maciej Dołęga Valentin Féray Piotr Śniady
+	A positivity conjecture for Jack polynomials	2007	Michel Lassalle
+ PDF Chat	A positivity conjecture for Jack polynomials	2008	Michel Lassalle
+	Positive formula for Jack polynomials, Jack characters and proof of Lassalle's conjecture	2023	Houcine Ben Dali Maciej Dołęga
+	Asymptotics of Jack characters	2019	Piotr Śniady
+	Gaussian Asymptotics of Jack Measures on Partitions from Weighted Enumeration of Ribbon Paths	2020	Alexander Von Moll
+ PDF Chat	Characters of symmetric groups in terms of free cumulants and Frobenius coordinates	2009	Maciej Dołęga Valentin Féray Piotr Śniady
+	Cumulants of Jack symmetric functions and the $b$-conjecture	2017	Maciej Dołęga Valentin Féray
+	Gaussian Asymptotics of Jack Measures on Partitions from Weighted Enumeration of Ribbon Paths	2020	Alexander Von Moll
+ PDF Chat	Cumulants of the q-semicircular law, Tutte polynomials, and heaps	2012	Matthieu Josuat-Vergès
+	Cumulant expansion for counting Eulerian orientations	2023	Mikhail Isaev Brendan D. McKay Rui-Ray Zhang

Works That Cite This (51)

Action	Title	Year	Authors
+	Cumulants of Jack symmetric functions and the $b$-conjecture	2017	Maciej Dołęga Valentin Féray
+ PDF Chat	The Top-Degree Part in the Matchings-Jack Conjecture	2021	Adam Burchardt
+	A recurrence formula for Jack connection coefficients	2014	A. L. Kanunnikov Ekaterina A. Vassilieva
+ PDF Chat	Superintegrability for ($$\beta $$-deformed) partition function hierarchies with W-representations	2022	Rui Wang Fan Liu Chun-Hong Zhang Wei‐Zhong Zhao
+	On higher deformed Calogero–Sutherland Hamiltonians	2024	Fu-Hao Zhang Fan Liu Yue Li Chun-Hong Zhang
+ PDF Chat	Narayana polynomials and Hall–Littlewood symmetric functions	2012	Michel Lassalle
+	Shifted symmetric functions and multirectangular coordinates of Young diagrams	2017	Per Alexandersson Valentin Féray
+	Zonal polynomials via Stanleyʼs coordinates and free cumulants	2011	Valentin Féray Piotr Śniady
+	Asymptotics of Jack characters	2019	Piotr Śniady
+	On Kerov polynomials for Jack characters	2012	Maciej Dołęga Valentin Féray

Works Cited by This (24)

Action	Title	Year	Authors
+	Symmetric Functions and Combinatorial Operators on Polynomials	2003	Alain Lascoux
+ PDF Chat	None	1998	Andreĭ Okounkov
+	Shifted Schur Functions	1996	Andreĭ Okounkov Grigori Olshanski
+	Two positivity conjectures for Kerov polynomials	2008	Michel Lassalle
+	Addition of certain non-commuting random variables	1986	Dan Voiculescu
+	Une q-spécialisation pour les fonctions symétriques monomiales	2001	Michel Lassalle
+	A recursion and a combinatorial formula for Jack polynomials	1997	Friedrich Knop Siddhartha Sahi
+	Transition probabilities for continual young diagrams and the Markov moment problem	1993	S. V. Kerov
+ PDF Chat	An explicit form for Kerov's character polynomials	2007	I. P. Goulden Amarpreet Rattan
+ PDF Chat	Combinatorial interpretation and positivity of Kerov’s character polynomials	2008	Valentin Féray