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

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 $q$ and the $\tau$-enumeration of Plane Partitions with specific symmetries, with $\tau=-(q+q^{-1})$. We also find a conjectural relation \`a la Razumov-Stroganov between the $\tau\to 0$ 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

The Perceived Impact of the In-Trust Agreements on CGIAR Germplasm Availability: An Assessment of Bioversity International's Institutional Activities

This study assesses the generation and consequences of the In-Trust Agreements (ITAs) that established the legal status of the CGIAR germplasm as freely available for the benefit of humanity under the auspices of FAO. The analysis looks at the history of the ITAs and focuses on the role of Bioversity International in research and other activities in influencing, facilitating and enabling the ITA negotiations. Results confirm the central role of Bioversity and policy research in the negotiations process. Concepts developed during the ITA negotiations contributed toward subsequent multilateral negotiations that eventually culminated in the International Treaty on Plant Genetic Resources

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

Determinant Formulae for some Tiling Problems and Application to Fully Packed Loops

We present determinant formulae for the number of tilings of various domains in relation with Alternating Sign Matrix and Fully Packed Loop enumeration

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

The sums of components of the ground states of the O(1) loop model on a cylinder or of the XXZ quantum spin chain at Delta=-1/2 (of size L) are expressed in terms of combinatorial numbers. The methods include the introduction of spectral parameters and the use of integrability, a mapping from size L to L+1, and knot-theoretic skein relations.Comment: final version to be publishe

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