Paul Zinn-Justin

Littlewood-Richardson coefficients for Grothendieck polynomials from integrability

Michael Wheeler, Paul Zinn-Justin

Journal article  |  2019  |  Journal für die reine und angewandte Mathematik (Crelles Journal)

Abstract We study the Littlewood–Richardson coefficients of double Grothendieck polynomials indexed by Grassmannian pe..

1324-avoiding permutations revisited

Andrew R Conway, Anthony J Guttmann, Paul Zinn-Justin

Journal article  |  2018  |  Advances in Applied Mathematics

Refined Cauchy/Littlewood identities and six-vertex model partition functions: III. Deformed bosons

Michael Wheeler, Paul Zinn-Justin

Journal article  |  2016  |  Advances in Mathematics

Theta function solutions of the quantum Knizhnik-Zamolodchikov-Bernard equation for a face model

Peter E Finch, Robert Weston, Paul Zinn-Justin

Journal article  |  2016  |  Journal of Physics A: Mathematical and Theoretical

Type (C)over-cap Brauer loop schemes and loop model with boundaries

Anita Ponsaing, Paul Zinn-Justin

Journal article  |  2016  |  Annales de l’Institut Henri Poincaré D

Quiver varieties and the quantum Knizhnik-Zamolodchikov equation

P Zinn-Justin

Journal article  |  2015  |  Theoretical and Mathematical Physics

Refined Cauchy/Littlewood identities and six-vertex model partition functions: II. Proofs and new conjectures

D Betea, M Wheeler, P Zinn-Justin

Journal article  |  2015  |  Journal of Algebraic Combinatorics

Knot theory and matrix integrals

P ZINN-JUSTIN, JB Zuber

Book Chapter  |  2015

With a foreword by Freeman Dyson, the handbook brings together leading mathematicians and physicists to offer a comprehensive over..

Equilibrium problems for Raney densities

Peter J Forrester, Dang-Zheng Liu, Paul Zinn-Justin

Journal article  |  2015  |  Nonlinearity

Higher Spin Polynomial Solutions of Quantum Knizhnik-Zamolodchikov Equation

Tiago Fonseca, Paul Zinn-Justin

Journal article  |  2014  |  Communications in Mathematical Physics

The Brauer loop scheme and orbital varieties

Allen Knutson, Paul Zinn-Justin

Journal article  |  2014  |  Journal of Geometry and Physics

Discrete holomorphicity and quantized affine algebras

Y Ikhlef, R Weston, M Wheeler, P Zinn-Justin

Journal article  |  2013  |  Journal of Physics A: Mathematical and Theoretical

A doubly-refined enumeration of alternating sign matrices and descending plane partitions

Roger E Behrend, Philippe Di Francesco, Paul Zinn-Justin

Journal article  |  2013  |  Journal of Combinatorial Theory, Series A

Sum rule for the eight-vertex model on its combinatorial line

P Zinn-Justin

Book Chapter  |  2013  |  Springer Proceedings in Mathematics and Statistics

Loop Models, Random Matrices and Planar Algebras

A Guionnet, VFR Jones, D Shlyakhtenko, P Zinn-Justin

Journal article  |  2012  |  Communications in Mathematical Physics

Extended Joseph polynomials, quantized conformal blocks, and a q-Selberg type integral

R Rimanyi, V Tarasov, A Varchenko, P Zinn-Justin

Journal article  |  2012  |  Journal of Geometry and Physics

Path representation of maximal parabolic Kazhdan-Lusztig polynomials

Keiichi Shigechi, Paul Zinn-Justin

Journal article  |  2012  |  Journal of Pure and Applied Algebra

On the weighted enumeration of alternating sign matrices and descending plane partitions

Roger E Behrend, Philippe Di Francesco, Paul Zinn-Justin

Journal article  |  2012  |  Journal of Combinatorial Theory, Series A

A conjectured formula for fully packed loop configurations in a triangle

P Zinn-Justin

Journal article  |  2010  |  Electronic Journal of Combinatorics

Integrability and combinatorics: selected topics

P ZINN-JUSTIN

Book Chapter  |  2010

This book of lectures by international leaders in the field sets these issues into a larger and more coherent theoretical perspect..

The arctic curve of the domain wall six-vertex model in its antiferroelectric regime

F Colomo, AG Pronko, P Zinn-Justin

Journal article  |  2010  |  Journal of Statistical Mechanics: Theory and Experiment

Jucys-Murphy Elements and Weingarten Matrices

Paul Zinn-Justin

Journal article  |  2010  |  Letters in Mathematical Physics

Six-vertex, Loop and Tiling Models Integrability and Combinatorics

Paul ZINN-JUSTIN

Book  |  2010

Punctured plane partitions and the q-deformed Knizhnik-Zamolodchikov and Hirota equations

Jan de Gier, Pavel Pyatov, Paul Zinn-Justin

Journal article  |  2009  |  Journal of Combinatorial Theory Series A

On some ground state components of the O(1) loop model

Tiago Fonseca, Paul Zinn-Justin

Journal article  |  2009  |  Journal of Statistical Mechanics: Theory and Experiment

Littlewood-Richardson coefficients and integrable tilings

Paul Zinn-Justin

Journal article  |  2009  |  Electronic Journal of Combinatorics

Spectral Analysis of the Free Orthogonal Matrix

Teodor Banica, Benoit Collins, Paul Zinn-Justin

Journal article  |  2009  |  International Mathematics Research Notices

On the doubly refined enumeration of alternating sign matrices and totally symmetric self-complementary plane partitions

Tiago Fonseca, Paul Zinn-Justin

Journal article  |  2008  |  Electronic Journal of Combinatorics

Quantum Knizhnik-Zamolodchikov equation, totally symmetric self-complementary plane partitions, and alternating sign matrices

P Zinn-Justin, P Di Francesco

Journal article  |  2008  |  Theoretical and Mathematical Physics

Quantum Knizhnik-Zamolodchikov equation: reflecting boundary conditions and combinatorics

P Di Francesco, P Zinn-Justin

Journal article  |  2007  |  Journal of Statistical Mechanics: Theory and Experiment

Polynomial solutions of qKZ equation and ground state of XXZ spin chain at Delta = -1/2

AV Razumov, Yu G Stroganov, P Zinn-Justin

Journal article  |  2007  |  Journal of Physics A: Mathematical and Theoretical

A scheme related to the Brauer loop model

A Knutson, P Zinn-Justin

Journal article  |  2007  |  Advances in Mathematics

Combinatorial point for fused loop models

P Zinn-Justin

Journal article  |  2007  |  Communications in Mathematical Physics

Loop model with mixed boundary conditions, qKZ equation and alternating sign matrices

P Zinn-Justin

Journal article  |  2007  |  Journal of Statistical Mechanics: Theory and Experiment

From orbital varieties to Alternating Sign Matrices

P Di Francesco, P Zinn-Justin

Conference Proceedings  |  2006  |  FPSAC 2006 - Proceedings: 18th Annual International Conference on Formal Power Series and Algebraic Combinatorics

Proof of the Razumov-Stroganov conjecture for some infinite families of link patterns

P Zinn-Justin

Journal article  |  2006  |  Electronic Journal of Combinatorics

Sum rules for the ground states of the O(1) loop model on a cylinder and the XXZ spin chain

P Di Francesco, P Zinn-Justin, JB Zuber

Journal article  |  2006  |  Journal of Statistical Mechanics: Theory and Experiment

Inhomogenous model of crossing loops and multidegrees of some algebraic varieties

P Di Francesco, P Zinn-Justin

Journal article  |  2006  |  Communications in Mathematical Physics

The quantum Knizhnik-Zamolodchikov equation, generalized Razumov-Stroganov sum rules and extended Joseph polynomials

P Di Francesco, P Zinn-Justin

Journal article  |  2005  |  Journal of Physics A: Mathematical and General

Around the Razumov-Stroganov conjecture: Proof of a multi-parameter sum rule

P Di Francesco, P Zinn-Justin

Journal article  |  2005  |  Electronic Journal of Combinatorics

Determinant formulae for some tiling problems and application to fully packed loops

P Di Francesco, P Zinn-Justin, JB Zuber

Journal article  |  2005  |  Annales de l’institut Fourier

Conjectures on the enumeration of alternating links

P ZINN-JUSTIN

Book Chapter  |  2005

This volume presents several contributions from researchers using computers to study problems that would otherwise be intractable.

A bijection between classes of fully packed loops and plane partitions

P Di Francesco, P Zinn-Justin, JB Zuber

Journal article  |  2004  |  Electronic Journal of Combinatorics

Algebraic bethe ansatz for the FPL2 model

J Jacobsen, P Zinn-Justin

Journal article  |  2004  |  Journal of Physics A: Mathematical and General

Matrix integrals and the generation and counting of virtual tangles and links

P Zinn-Justin, JB Zuber

Journal article  |  2004  |  Journal of Knot Theory and Its Ramifications

Virtual links are generalizations of classical links that can be represented by links embedded in a "thickened" surface Σ×I, produ..

On the asymptotic number of plane curves and alternating knots

G Schaeffer, P Zinn-Justin

Journal article  |  2004  |  Experimental Mathematics

The asymmetric ABAB matrix model

P Zinn-Justin

Journal article  |  2003  |  Europhysics Letters (EPL)

The combinatorics of alternating tangles: from theory to computerized enumeration

P ZINN-JUSTIN, J Jacobsen

Book Chapter  |  2003

A European Mathematical Summer School held at the Euler Institute, St. Petersburg, Russia, July 9-20, 2001 Anatoly M. ... point p..

On some integrals over the U(N) unitary group and their large N limit

P Zinn-Justin, JB Zuber

Journal article  |  2003  |  Journal of Physics A: Mathematical and General

The general O(n) quartic matrix model and its application to counting tangles and links

P Zinn-Justin

Journal article  |  2003  |  Communications in Mathematical Physics

The general O(n) quartic matrix model and its application to counting tangles and links

P Zinn-Justin

Journal article  |  2003  |  Communications in Mathematical Physics

Matrix models and the enumeration of alternating tangles

P ZINN-JUSTIN, J Jacobsen

Journal article  |  2003  |  Markov Processes and Related Fields

Monochromatic path crossing exponents and graph connectivity in two-dimensional percolation.

Jesper Lykke Jacobsen, Paul Zinn-Justin

Journal article  |  2002  |  Physical Review E

We consider the fractal dimensions d(k) of the k-connected part of percolation clusters in two dimensions, generalizing the cluste..

A transfer matrix approach to the enumeration of knots

JL Jacobsen, P Zinn-Justin

Journal article  |  2002  |  Journal of Knot Theory and Its Ramifications

We propose a new method to enumerate alternating knots using a transfer matrix approach. We apply it to count numerically various ..

HCIZ integral and 2D Toda lattice hierarchy

P Zinn-Justin

Journal article  |  2002  |  Nuclear Physics B

Inhomogeneous six-vertex model with domain wall boundary conditions and Bethe ansatz

V Korepin, P Zinn-Justin

Journal article  |  2002  |  Journal of Mathematical Physics

A transfer matrix for the backbone exponent of two-dimensional percolation

JL Jacobsen, P Zinn-Justin

Journal article  |  2002  |  Journal of Physics A: Mathematical and General

Matrix integrals and the counting of tangles and links

P Zinn-Justin, JB Zuber

Journal article  |  2002  |  Discrete Mathematics

A Transfer Matrix approach to the Enumeration of Colored Links

JL Jacobsen, P Zinn-Justin

Journal article  |  2001  |  Journal of Knot Theory and Its Ramifications

We propose a transfer matrix algorithm for the enumeration of alternating link diagrams with external legs, giving a weight n to e..

Some matrix integrals related to knots and links

P ZINN-JUSTIN

Book Chapter  |  2001

Expository articles on random matrix theory emphasizing the exchange of ideas between the physical and mathematical communities.

Thermodynamic limit of the six-vertex model with domain wall boundary conditions

V Korepin, P Zinn-Justin

Journal article  |  2000  |  Journal of Physics A: Mathematical and General

Thermodynamic limit of the six-vertex model with domain wall boundary conditions

V Korepin, P Zinn-Justin

Journal article  |  2000  |  Journal of Physics A: Mathematical and General

Six-vertex model with domain wall boundary conditions and one-matrix model

P Zinn-Justin

Journal article  |  2000  |  Physical Review E

The six-vertex model on random lattices

P Zinn-Justin

Journal article  |  2000  |  Europhysics Letters (EPL)

On the counting of colored tangles

P Zinn-Justin, JB Zuber

Journal article  |  2000  |  Journal of Knot Theory and Its Ramifications

The connection between matrix integrals and links is used to define matrix models which count alternating tangles n which each clo..

The dilute potts model on random surfaces

P Zinn-Justin

Journal article  |  2000  |  Journal of Statistical Physics

Two-matrix model with ABAB interaction

VA Kazakov, P Zinn-Justin

Journal article  |  1999  |  Nuclear Physics B

Adding and multiplying random matrices: A generalization of Voiculescu's formulas

P Zinn-Justin

Journal article  |  1999  |  Physical Review E

The generalized multi-channel Kondo model: Thermodynamics and fusion equations

P Zinn-Justin, N Andrei

Journal article  |  1998  |  Nuclear Physics B

Nonlinear integral equations for complex affine Toda models associated with simply laced Lie algebras

P Zinn-Justin

Journal article  |  1998  |  Journal of Physics A: Mathematical and General

Universality of correlation functions of Hermitian random matrices in an external field

P Zinn-Justin

Journal article  |  1998  |  Communications in Mathematical Physics

Random Hermitian matrices in an external field

P Zinn-Justin

Journal article  |  1997  |  Nuclear Physics B