Quadratic Equations over Finite Fields and Class Numbers of Real Quadratic Fields.
Quasi-particle fermionic formulas for (k, 3)-admissible configurations
We construct new monomial quasi-particle bases of Feigin-Stoyanovsky type subspaces for the affine Lie algebra sl(3;ℂ)∧ from which the known fermionic-type formulas for (k, 3)-admissible configurations follow naturally. In the proof we use vertex operator algebra relations for standard modules and coefficients of intertwining operators.
Quelques valeurs prises par les polynômes de Macdonald décalés
Nous explicitons la valeur de certains des coefficients binomiaux généralisés associés aux polynômes de Macdonald, c’est-à-dire la valeur en certains points particuliers des polynômes de Macdonald décalés. Ces expressions font intervenir les fonctions hypergéométriques de base .
Quintuple products and Ramanujan's partition congruence p(11n+6) ≡ 0(mod 11)
Rainbow 3-term arithmetic progressions.
Ramanujan grammar and Cayley trees. (Grammaire de Ramanujan et arbres de Cayley.)
Ramanujan type congruences for a partition function.
Ramanujan's method in -series congruences.
Ramified Sets Of Pseudotrees
Ramified sets or pseudotrees.
Random matrices and permutations, matrix integrals and integrable systems
Random matrices, magic squares and matching polynomials.
Random orders and gambler's ruin.
Random walk on a building of type Ãr and brownian motion of the Weyl chamber
In this paper we study a random walk on an affine building of type Ãr, whose radial part, when suitably normalized, converges toward the brownian motion of the Weyl chamber. This gives a new discrete approximation of this process, alternative to the one of Biane (Probab. Theory Related Fields89 (1991) 117–129). This extends also the link at the probabilistic level between riemannian symmetric spaces of the noncompact type and their discrete counterpart, which had been previously discovered by Bougerol...
Random Young tableaux and combinatorial identities.
Rare events and conditional events on random strings.
Ratio monotonicity of polynomials derived from nondecreasing sequences.
Rational identities and inequalities.
Rationality, irrationality, and Wilf equivalence in generalized factor order.
rc-graphs and Schubert polynomials.