We give closed combinatorial product formulas for Kazhdan–Lusztig poynomials and their parabolic analogue of type q in the case of boolean elements, introduced in [M. Marietti, Boolean elements in Kazhdan–Lusztig theory, J. Algebra 295 (2006)], in Coxeter groups whose Coxeter graph is a tree. Such formulas involve Catalan numbers and use a combinatorial interpretation of the Coxeter graph of th...

This paper outlines the “Pyrénées Itinéraires Virtuels” project. The aim of this project is to add value to a legacy localised corpus. Unified models are proposed to define spatial entities in a formal way. These models allow to build a specific information retrieval system based on the semantic contents of various kinds of documents. Moreover, a reflection on computable interpretation of these...

In this paper we give a graph theoretic combinatorial interpretation for the cluster variables that arise in most cluster algebras of finite type. In particular, we provide a family of graphs such that a weighted enumeration of their perfect matchings encodes the numerator of the associated Laurent polynomial while decompositions of the graphs correspond to the denominator. This complements rec...