Probabilities as values of modular forms and continued fractions.
Probability measures corresponding to Aval numbers
We describe the class of probability measures whose moments are given in terms of the Aval numbers. They are expressed as the multiplicative free convolution of measures corresponding to the ballot numbers .
Probability that an element of a finite group has a square root
Let G be a finite group of even order. We give some bounds for the probability p(G) that a randomly chosen element in G has a square root. In particular, we prove that p(G) ≤ 1 - ⌊√|G|⌋/|G|. Moreover, we show that if the Sylow 2-subgroup of G is not a proper normal elementary abelian subgroup of G, then p(G) ≤ 1 - 1/√|G|. Both of these bounds are best possible upper bounds for p(G), depending only on the order of G.
Problemas combinatorios sobre bases aditivas.
Problemas da teoria dos grafos e a sua relação com os problemas da cobertura e da partição de um conjunto
Procédures optimales pour le classement des meilleurs articles parmi au moyen de comparaisons binaires
Product and puzzle formulae for Belkale-Kumar coefficients.
Product partitions and recursion formulae.
Profile classes and partial well-order for permutations.
Profiles of permutations.
Proof of a conjecture of Chan, Robbins, and Yuen.
Proof of a conjecture of Hirschhorn and Sellers on overpartitions
Let p̅(n) denote the number of overpartitions of n. It was conjectured by Hirschhorn and Sellers that p̅(40n+35) ≡ 0 (mod 40) for n ≥ 0. Employing 2-dissection formulas of theta functions due to Ramanujan, and Hirschhorn and Sellers, we obtain a generating function for p̅(40n+35) modulo 5. Using the (p, k)-parametrization of theta functions given by Alaca, Alaca and Williams, we prove the congruence p̅(40n+35) ≡ 0 (mod 5) for n ≥ 0. Combining this congruence and the congruence p̅(4n+3) ≡ 0 (mod...
Proof of a determinant evaluation conjectured by Bombieri, Hunt and van Poorten.
Proof of Conway's lost cosmological theorem.
Proof of the alternating sign matrix conjecture.
Proof of the Macdonald Conjecture.
Proof of the Razumov-Stroganov conjecture for some infinite families of link patterns.
Proof of the refined alternating sign matrix conjecture.
Properties of the van der Pol numbers and polynomials.
Propriétés arithmétiques des polynômes d'Euler