Philippe Di Francesco

1987 …2019
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Research Output 1987 2019

2019
Quantum Algebra
algebra
operators
Algebra
Affine Hecke Algebra
tangents
Tangent line
derivation
Path
Curve

The Arctic Curve for Aztec Rectangles with Defects via the Tangent Method

Di Francesco, P. & Guitter, E., Aug 15 2019, In : Journal of Statistical Physics. 176, 3, p. 639-678 40 p.

Research output: Contribution to journalArticle

rectangles
tangents
Rectangle
Tangent line
Defects
2018

Arctic curves for paths with arbitrary starting points: A tangent method approach

Di Francesco, P. & Guitter, E., Jul 20 2018, In : Journal of Physics A: Mathematical and Theoretical. 51, 35, 355201.

Research output: Contribution to journalArticle

tangents
Freezing
Tangent line
Path
Curve

Arctic curves in path models from the tangent method

Di Francesco, P. & Lapa, M. F., Mar 19 2018, In : Journal of Physics A: Mathematical and Theoretical. 51, 15, 155202.

Research output: Contribution to journalArticle

tangents
Tangent line
Alternating Sign Matrices
Rhombus
Lattice Paths

DIFFERENCE EQUATIONS FOR GRADED CHARACTERS FROM QUANTUM CLUSTER ALGEBRA

Di Francesco, P. & Kedem, R., Jun 1 2018, In : Transformation Groups. 23, 2, p. 391-424 34 p.

Research output: Contribution to journalArticle

Cluster Algebra
Quantum Algebra
Difference equation
Conserved Quantity
Module

OPE for XXX

Di Francesco, P. & Smirnov, F., Jul 1 2018, In : Reviews in Mathematical Physics. 30, 6, 1840006.

Research output: Contribution to journalArticle

operators
expansion
Spin Chains
Guess
coefficients

OPE for XXX

Di Francesco, P. & Smirnov, F., Jan 1 2018, Ludwig Faddeev Memorial Volume: A Life in Mathematical Physics. World Scientific Publishing Co., p. 183-200 18 p.

Research output: Chapter in Book/Report/Conference proceedingChapter

operators
expansion
Spin Chains
Guess
coefficients
2017

A path model for Whittaker vectors

Di Francesco, P., Kedem, R. & Turmunkh, B., 2017, In : Journal of Physics A: Mathematical and Theoretical. 50, 25, p. 255201, 35

Research output: Contribution to journalArticle

Quantum Q systems: from cluster algebras to quantum current algebras

Di Francesco, P. & Kedem, R., Feb 1 2017, In : Letters in Mathematical Physics. 107, 2, p. 301-341 41 p.

Research output: Contribution to journalArticle

Current Algebra
Cluster Algebra
current algebra
Quantum Algebra
algebra

Systematic procedure for analyzing cumulants at any order

Di Francesco, P., Guilbaud, M., Luzum, M. & Ollitrault, J. Y., Apr 24 2017, In : Physical Review C. 95, 4, 044911.

Research output: Contribution to journalArticle

ionic collisions
nonuniformity
baryons
detectors
2015

Bessenrodt-Stanley polynomials and the octahedron recurrence

Di Francesco, P., Sep 11 2015, In : Electronic Journal of Combinatorics. 22, 3, #P3.35.

Research output: Contribution to journalArticle

Octahedron
Multivariate Polynomials
Dimer
Partition Function
Dimers

The Non-Commutative A 1 T-System and its Positive Laurent Property

Di Francesco, P., Jan 1 2015, In : Communications in Mathematical Physics. 335, 2, p. 935-953 19 p.

Research output: Contribution to journalArticle

hexagons
entry
ladders
integers
partitions
2014

Arctic curves of the octahedron equation

Francesco, P. D. & Soto-Garrido, R., Jan 1 2014, In : Journal of Physics A: Mathematical and Theoretical. 47, 28, 285204.

Research output: Contribution to journalArticle

Octahedron
Dimer
Dimers
dimers
Curve

Cluster algebras in mathematical physics

Di Francesco, P., Gekhtman, M., Kuniba, A. & Yamazaki, M., Nov 28 2014, In : Journal of Physics A: Mathematical and Theoretical. 47, 47, 470301.

Research output: Contribution to journalEditorial

Cluster Algebra
Algebra
algebra
Physics
physics

Quantum cluster algebras and fusion products

Di Francesco, P. & Kedem, R., 2014, In : International Mathematics Research Notices. 2014, 10, p. 2593-2642 50 p.

Research output: Contribution to journalArticle

Cluster Algebra
Quantum Algebra
Fusion
Quantum Affine Algebra
Recursion Relations

Special issue on cluster algebras in mathematical physics

Di Francesco, P., Gekhtman, M., Kuniba, A. & Yamazaki, M., 2014, In : Journal of Physics A: Mathematical and Theoretical. 47, 10, p. 100201, 2

Research output: Contribution to journalArticle

T-Systems, Networks and Dimers

Di Francesco, P., Nov 2014, In : Communications in Mathematical Physics. 331, 3, p. 1237-1270 34 p.

Research output: Contribution to journalArticle

Dimer
Hexahedron
dimers
Octahedron
Transfer Operator
2013

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

Behrend, R. E., Di Francesco, P. & Zinn-Justin, P., Feb 1 2013, In : Journal of Combinatorial Theory. Series A. 120, 2, p. 409-432 24 p.

Research output: Contribution to journalArticle

Alternating Sign Matrices
Plane Partitions
Enumeration
Statistics
Statistic

An inhomogeneous Lambda-determinant

Di Francesco, P., Aug 16 2013, In : Electronic Journal of Combinatorics. 20, 3, P19.

Research output: Contribution to journalArticle

Alternating Sign Matrices
Cluster Algebra
Weighted Sums
Recurrence
Algebra

Integrable combinatorics

Di Francesco, P., Jan 1 2013, XVIIth International Congress on Mathematical Physics: Aalborg, Denmark, 6-11 August 2012. World Scientific Publishing Co., p. 29-51 23 p.

Research output: Chapter in Book/Report/Conference proceedingChapter

T-systems with boundaries from network solutions

Di Francesco, P. & Kedem, R., Jan 7 2013, In : Electronic Journal of Combinatorics. 20, 1

Research output: Contribution to journalArticle

Algebra
Boundary conditions
Pentagram
Octahedron
Cluster Algebra
2012

Asymptotic Shapes with Free Boundaries

Di Francesco, P. & Reshetikhin, N., Jan 1 2012, In : Communications in Mathematical Physics. 309, 1, p. 87-121 35 p.

Research output: Contribution to journalArticle

free boundaries
Free Boundary
Random Surfaces
Hexagonal Lattice
Dimer

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

Behrend, R. E., Di Francesco, P. & Zinn-Justin, P., Feb 1 2012, In : Journal of Combinatorial Theory. Series A. 119, 2, p. 331-363 33 p.

Research output: Contribution to journalArticle

Alternating Sign Matrices
Plane Partitions
Enumeration
Determinant
Bijection

The Solution of the Quantum A 1 T-System for Arbitrary Boundary

Di Francesco, P. & Kedem, R., Jul 1 2012, In : Communications in Mathematical Physics. 313, 2, p. 329-350 22 p.

Research output: Contribution to journalArticle

Liouville equations
Arbitrary
mutations
algebra
Cluster Algebra
2011

Discrete Integrable Systems, Positivity, and Continued Fraction Rearrangements

Di Francesco, P., Jun 1 2011, In : Letters in Mathematical Physics. 96, 1-3, p. 299-324 26 p.

Research output: Contribution to journalReview article

Integrable Systems
mutations
Continued fraction
Rearrangement
Discrete Systems

Introduction and guide to the handbook

Akemann, G., Baik, J. & Di Francesco, P., 2011, The Oxford handbook of random matrix theory. Oxford Univ. Press, Oxford, p. 3-14 12 p.

Research output: Chapter in Book/Report/Conference proceedingOther chapter contribution

Non-commutative integrability, paths and quasi-determinants

Di Francesco, P. & Kedem, R., Sep 10 2011, In : Advances in Mathematics. 228, 1, p. 97-152 56 p.

Research output: Contribution to journalArticle

Integrability
Determinant
Path
Cluster Algebra
Discrete Equations

Quantum $A_r$ $Q$-system solutions as q-multinomial series

Di Francesco, P., 2011, In : Electronic Journal of Combinatorics. 18, 1, p. Paper 176, 17

Research output: Contribution to journalArticle

Quantum Ar Q-system solutions as q-multinomial series

di Francesco, P., Sep 19 2011, In : Electronic Journal of Combinatorics. 18, 1, p. 1-17 17 p.

Research output: Contribution to journalArticle

Data structures
Multinomial Coefficients
Series
Integrability
Data Structures
2010

Discrete non-commutative integrability: Proof of a conjecture by M. Kontsevich

Di Francesco, P. & Kedem, R., Nov 11 2010, In : International Mathematics Research Notices. 2010, 21, p. 4042-4063 22 p.

Research output: Contribution to journalArticle

Integrability
Positive Polynomials
Cluster Algebra
Laurent Polynomials
Recursion Relations
Total Positivity
Cluster Algebra
Totally Positive Matrices
Path
Weighted Graph

The solution of the $A_r$ $T$-system for arbitrary boundary

Di Francesco, P., 2010, In : Electronic Journal of Combinatorics. 17, 1, p. Research Paper 89, 43

Research output: Contribution to journalArticle

The solution of the Ar T-system for arbitrary boundary

Di Francesco, P., Aug 20 2010, In : Electronic Journal of Combinatorics. 17, 1, p. 1-43 43 p.

Research output: Contribution to journalArticle

Laurent Polynomials
Arbitrary
Explicit Solution
Partition Function
Non-negative
2009

Positivity of the $T$-system cluster algebra

Di Francesco, P. & Kedem, R., 2009, In : Electronic Journal of Combinatorics. 16, 1, p. Research Paper 140, 39

Research output: Contribution to journalArticle

Q-Systems, heaps, paths and cluster positivity

Di Francesco, P. & Kedem, R., Dec 1 2009, In : Communications in Mathematical Physics. 293, 3, p. 727-802 76 p.

Research output: Contribution to journalArticle

Heap
Positivity
Partition Function
partitions
Path
Cartan Matrix
Cluster Algebra
Finite Type
polynomials
algebra
2008

Proof of the combinatorial kirillov-Reshetikhin conjecture

Francesco, P. D. & Kedem, R., Dec 1 2008, In : International Mathematics Research Notices. 2008, 1, rnn006.

Research output: Contribution to journalArticle

Tensor Product
Multiplicity
Simple Lie Algebra
Summation
Generating Function
Alternating Sign Matrices
Plane Partitions
partitions
polynomials
Polynomial Solutions
2007

Blocked edges on Eulerian maps and mobiles: Application to spanning trees, hard particles and the Ising model

Bouttier, J., Di Francesco, P. & Guitter, E., Jul 6 2007, In : Journal of Physics A: Mathematical and Theoretical. 40, 27, p. 7411-7440 30 p., 002.

Research output: Contribution to journalArticle

Quadrangulation
Ising model
Mobile Applications
Spanning tree
Ising Model

Correlation functions of Harish-Chandra integrals over the orthogonal and the symplectic groups

Ferrer, A. P., Eynard, B., Di Francesco, P. & Zuber, J. B., Oct 1 2007, In : Journal of Statistical Physics. 129, 5-6, p. 885-935 51 p.

Research output: Contribution to journalArticle

Symplectic Group
Correlation Function
Compact Group
matrices
Triangular matrix

Mass distribution exponents for growing trees

David, F., Di Francesco, P., Guitter, E. & Jonsson, T., Feb 1 2007, In : Journal of Statistical Mechanics: Theory and Experiment. 2, P02011.

Research output: Contribution to journalArticle

mass distribution
Exponent
exponents
apexes
attachment
Plane Partitions
enumeration
Enumeration
partitions
Symmetry
Plane Partitions
enumeration
Transpose
Integral Formula
Combinatorics
2006

2D quantum gravity, matrix models and graph combinatorics

Di Francesco, P., 2006, Applications of random matrices in physics. Springer, Dordrecht, Vol. 221. p. 33-88 56 p. (NATO Sci. Ser. II Math. Phys. Chem.).

Research output: Chapter in Book/Report/Conference proceedingOther chapter contribution

From orbital varieties to Alternating Sign Matrices

Di Francesco, P. & Zinn-Justin, P., Dec 1 2006, p. 95-107. 13 p.

Research output: Contribution to conferencePaper

Alternating Sign Matrices
Plane Partitions
Associated Polynomials
Integrable Models
Simple Lie Algebra

Inhomogenous model of crossing loops and multidegrees of some algebraic varieties

Di Francesco, P. & Zinn-Justin, P., Mar 1 2006, In : Communications in Mathematical Physics. 262, 2, p. 459-487 29 p.

Research output: Contribution to journalArticle

Brauer Algebra
Sum Rules
Algebraic Variety
entry
Eigenvector

Multicritical continuous random trees

Bouttier, J., Di Francesco, P. & Guitter, E., Apr 1 2006, In : Journal of Statistical Mechanics: Theory and Experiment. 4, P04004.

Research output: Contribution to journalArticle

Random Trees
Scaling Limit
Branching
Integral Formula
Hypergeometric Functions

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

Di Francesco, P., Zinn-Justin, P. & Zuber, J. B., Aug 1 2006, In : Journal of Statistical Mechanics: Theory and Experiment. 8, P08011.

Research output: Contribution to journalArticle

Spin Chains
Sum Rules
sum rules
Ground State
Quantum Spin Chain
Plane Partitions
Minimal polynomial
enumeration
Polynomial Solutions
Enumeration