Philippe Di Francesco

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2019

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

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

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

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

OPE for XXX

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

Research output: Contribution to journalArticle

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

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

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

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

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

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

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

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

An inhomogeneous Lambda-determinant

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

Research output: Contribution to journalArticle

Open Access

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

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

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

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

2011

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

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

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

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

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

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

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

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

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

2006

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

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

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

2005

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

Di Francesco, P. & Zinn-Justin, P., Jan 11 2005, In : Electronic Journal of Combinatorics. 12, 1 R, p. 1-27 27 p., R6.

Research output: Contribution to journalArticle

Combinatorics of bicubic maps with hard particles

Bouttier, J., Di Francesco, P. & Guitter, E., May 27 2005, In : Journal of Physics A: Mathematical and General. 38, 21, p. 4529-4559 31 p.

Research output: Contribution to journalArticle

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

Di Francesco, P., Zinn-Justin, P. & Zuber, J. B., Jan 1 2005, In : Annales de l'Institut Fourier. 55, 6, p. 2025-2050+XX+XXVI

Research output: Contribution to journalArticle

Geodesic distance in planar graphs: An integrable approach

Di Francesco, P., Oct 1 2005, In : Ramanujan Journal. 10, 2, p. 153-186 34 p.

Research output: Contribution to journalArticle

Inhomogeneous loop models with open boundaries

Di Francesco, P., Jul 8 2005, In : Journal of Physics A: Mathematical and General. 38, 27, p. 6091-6120 30 p.

Research output: Contribution to journalArticle

Integrability of graph combinatorics via random walks and heaps of dimers

Di Francesco, P. & Guitter, E., Sep 1 2005, In : Journal of Statistical Mechanics: Theory and Experiment. 9, p. 29-62 34 p.

Research output: Contribution to journalArticle