Determinantal expression and recursion for Jack polynomials.
Determinantal generating functions of colored spanning forests.
Determinantal transition kernels for some interacting particles on the line
We find the transition kernels for four markovian interacting particle systems on the line, by proving that each of these kernels is intertwined with a Karlin–McGregor-type kernel. The resulting kernels all inherit the determinantal structure from the Karlin–McGregor formula, and have a similar form to Schütz’s kernel for the totally asymmetric simple exclusion process.
Déterminants et intégrales de Fresnel
On présente ici une approche directe et géométrique pour le calcul des déterminants d’opérateurs de type Schrödinger sur un graphe fini. Du calcul de l’intégrale de Fresnel associée, on déduit le déterminant. Le calcul des intégrales de Fresnel est grandement facilité par l’utilisation simultanée du théorème de Fubini et d’une version linéaire du calcul symbolique des opérateurs intégraux de Fourier. On obtient de façon directe une formule générale exprimant le déterminant en terme des conditions...
Determinants of (–1,1)-matrices of the skew-symmetric type: a cocyclic approach
An n by n skew-symmetric type (-1; 1)-matrix K =[ki;j ] has 1’s on the main diagonal and ±1’s elsewhere with ki;j =-kj;i . The largest possible determinant of such a matrix K is an interesting problem. The literature is extensive for n ≡ 0 mod 4 (skew-Hadamard matrices), but for n ≡ 2 mod 4 there are few results known for this question. In this paper we approach this problem constructing cocyclic matrices over the dihedral group of 2t elements, for t odd, which are equivalent to (-1; 1)-matrices...
Determinants of Latin squares of order 8.
Determinants of matrices related to the Pascal triangle
The aim of this paper is to study determinants of matrices related to the Pascal triangle.
Determination of all rigid groups of order not exceeding 60
Determination of Large Families and Diameter of Equiseparable Trees
Determination of the structure of algebraic curvature tensors by means of Young symmetrizers.
Determining lower bounds for packing densities of non-layered patterns using weighted templates.
Determining the maximal degree of a tree given by its distance matrix
Detour chromatic numbers
The nth detour chromatic number, χₙ(G) of a graph G is the minimum number of colours required to colour the vertices of G such that no path with more than n vertices is monocoloured. The number of vertices in a longest path of G is denoted by τ( G). We conjecture that χₙ(G) ≤ ⎡(τ(G))/n⎤ for every graph G and every n ≥ 1 and we prove results that support the conjecture. We also present some sufficient conditions for a graph to have nth chromatic number at most 2.
Deux propriétés combinatoires des nombres de Schröder
Deux propriétés combinatoires du langage de Lukasiewicz
Diagonal checker-jumping and Eulerian numbers for color-signed permutations.
Diagonal peg solitaire.
Diagonal similarity of matrices
Diagonal sums of boxed plane partitions.
Diagonal Temperley-Lieb invariants and harmonics.