4 citations · 10 across the 8 of their papers we have counts for
8 papers · 1 filter
Product-Coproduct Prographs and Triangulations of the Sphere
Nicolas Borie, Justine Falque
In this paper, we explain how the classical Catalan families of objects involving paths, tableaux, triangulations, parentheses configurations and more generalize canonically to a t…
Three-dimensional Catalan numbers and product-coproduct prographs
Nicolas Borie
We present the new combinatorial class of product-coproduct prographs which are planar assemblies of two types of operators: products having two inputs and a single output and copr…
The Hopf Algebra of graph invariants
Nicolas Borie
We propose an algebraic study of the simple graph isomorphism problem. We define a Hopf algebra from an explicit realization of its elements as formal power series. We show that th…
Effective Invariant Theory of Permutation Groups using Representation Theory
Nicolas Borie
Using the theory of representations of the symmetric group, we propose an algorithm to compute the invariant ring of a permutation group. Our approach have the goal to reduce the a…
Combinatorics of simple marked mesh patterns in 132-avoiding permutations
Nicolas Borie
We present some combinatorial interpretations for coefficients appearing in series partitioning the permutations avoiding 132 along marked mesh patterns. We identify for patterns i…
Generating tuples of integers modulo the action of a permutation group and applications
Nicolas Borie
Originally motivated by algebraic invariant theory, we present an algorithm to enumerate integer vectors modulo the action of a permutation group. This problem generalizes the gene…
An evaluation approach to computing invariants rings of permutation groups
Nicolas Borie, Nicolas M. Thiéry
Using evaluation at appropriately chosen points, we propose a Gröbner basis free approach for calculating the secondary invariants of a finite permutation group. This approach allo…
Deformed diagonal harmonic polynomials for complex reflection groups
François Bergeron, Nicolas Borie, Nicolas M. Thiéry
We introduce deformations of the space of (multi-diagonal) harmonic polynomials for any finite complex reflection group of the form W=G(m,p,n), and give supporting evidence that th…