84 citations · 521 across the 32 of their papers we have counts for
7 papers · 1 filter
From Orbital Varieties to Alternating Sign Matrices
P. Di Francesco, P. Zinn-Justin
We study a one-parameter family of vector-valued polynomials associated to each simple Lie algebra. When this parameter equals -1 one recovers Joseph polynomials, whereas at $q…
Boundary qKZ equation and generalized Razumov-Stroganov sum rules for open IRF models
P. Di Francesco
We find higher rank generalizations of the Razumov--Stroganov sum rules at for models with open boundaries, by constructing polynomial solutions of l…
Quantum Knizhnik-Zamolodchikov equation, generalized Razumov-Stroganov sum rules and extended Joseph polynomials
P. Di Francesco, P. Zinn-Justin
We prove higher rank analogues of the Razumov--Stroganov sum rule for the groundstate of the O(1) loop model on a semi-infinite cylinder: we show that a weighted sum of components…
Geodesic Distance in Planar Graphs: An Integrable Approach
P. Di Francesco
We discuss the enumeration of planar graphs using bijections with suitably decorated trees, which allow for keeping track of the geodesic distances between faces of the graph. The…
Geometrically constrained statistical systems on regular and random lattices: From folding to meanders
P. Di Francesco, E. Guitter
We review a number a recent advances in the study of two-dimensional statistical models with strong geometrical constraints. These include folding problems of regular and random la…
Inhomogeneous loop models with open boundaries
P. Di Francesco
We consider the crossing and non-crossing O(1) dense loop models on a semi-infinite strip, with inhomogeneities (spectral parameters) that preserve the integrability. We compute th…
Combinatorics of bicubic maps with hard particles
J. Bouttier, P. Di Francesco, E. Guitter
We present a purely combinatorial solution of the problem of enumerating planar bicubic maps with hard particles. This is done by use of a bijection with a particular class of blos…