7,674 research outputs found
Polynomial Fusion Rings of Logarithmic Minimal Models
We identify quotient polynomial rings isomorphic to the recently found
fundamental fusion algebras of logarithmic minimal models.Comment: 18 page
Planar maps as labeled mobiles
We extend Schaeffer's bijection between rooted quadrangulations and
well-labeled trees to the general case of Eulerian planar maps with prescribed
face valences, to obtain a bijection with a new class of labeled trees, which
we call mobiles. Our bijection covers all the classes of maps previously
enumerated by either the two-matrix model used by physicists or by the
bijection with blossom trees used by combinatorists. Our bijection reduces the
enumeration of maps to that, much simpler, of mobiles and moreover keeps track
of the geodesic distance within the initial maps via the mobiles' labels.
Generating functions for mobiles are shown to obey systems of algebraic
recursion relations.Comment: 31 pages, 17 figures, tex, lanlmac, epsf; improved tex
Statistics of planar graphs viewed from a vertex: A study via labeled trees
We study the statistics of edges and vertices in the vicinity of a reference
vertex (origin) within random planar quadrangulations and Eulerian
triangulations. Exact generating functions are obtained for theses graphs with
fixed numbers of edges and vertices at given geodesic distances from the
origin. Our analysis relies on bijections with labeled trees, in which the
labels encode the information on the geodesic distance from the origin. In the
case of infinitely large graphs, we give in particular explicit formulas for
the probabilities that the origin have given numbers of neighboring edges
and/or vertices, as well as explicit values for the corresponding moments.Comment: 36 pages, 15 figures, tex, harvmac, eps
Open boundary Quantum Knizhnik-Zamolodchikov equation and the weighted enumeration of Plane Partitions with symmetries
We propose new conjectures relating sum rules for the polynomial solution of
the qKZ equation with open (reflecting) boundaries as a function of the quantum
parameter and the -enumeration of Plane Partitions with specific
symmetries, with . We also find a conjectural relation \`a la
Razumov-Stroganov between the limit of the qKZ solution and refined
numbers of Totally Symmetric Self Complementary Plane Partitions.Comment: 27 pages, uses lanlmac, epsf and hyperbasics, minor revision
Entanglement Entropy of the Low-Lying Excited States and Critical Properties of an Exactly Solvable Two-Leg Spin Ladder with Three-Spin Interactions
In this work, we investigate an exactly solvable two-leg spin ladder with
three-spin interactions. We obtain analytically the finite-size corrections of
the low-lying energies and determine the central charge as well as the scaling
dimensions. The model considered in this work has the same universality class
of critical behavior of the XX chain with central charge c=1. By using the
correlation matrix method, we also study the finite-size corrections of the
Renyi entropy of the ground state and of the excited states. Our results are in
agreement with the predictions of the conformal field theory.Comment: 10 pages, 6 figures, 2 table
Quantum Knizhnik-Zamolodchikov equation: reflecting boundary conditions and combinatorics
We consider the level 1 solution of quantum Knizhnik-Zamolodchikov equation
with reflecting boundary conditions which is relevant to the Temperley--Lieb
model of loops on a strip. By use of integral formulae we prove conjectures
relating it to the weighted enumeration of Cyclically Symmetric Transpose
Complement Plane Partitions and related combinatorial objects
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