Add to ORKGWe present various results on the number of prime factors of the parts of a partition of an integer. We study the parity of this number, the extremal orders and we prove a Hardy-Ramanujan type theorem. These results show that for almost all partitions of an integer the sequence of the parts satisfies similar arithmetic properties as the sequence of natural numbers
AbstractRamanujanʼs famous partition congruences modulo powers of 5, 7, and 11 imply that certain se...
AbstractUsing elementary methods, we establish several new Ramanujan type identities and congruences...
This paper shows how to prove the Theorem = , i.e., the number of partitions of n into p-parts is e...
AbstractWe provide some further theorems on the partitions generated by the rank parity function. Ne...
International audienceImproving on some results of J.-L. Nicolas, the elements of the set ${\cal A}=...
International audienceImproving on some results of J.-L. Nicolas, the elements of the set ${\cal A}=...
International audienceImproving on some results of J.-L. Nicolas, the elements of the set ${\cal A}=...
International audienceImproving on some results of J.-L. Nicolas, the elements of the set ${\cal A}=...
12 pagesLet $d\ge 2$ be a fixed integer. We prove that a positive proportion of partitions of an int...
AbstractA new expansion is given for partial sums of Eulerʼs pentagonal number series. As a corollar...
International audienceLet $d\ge 2$ be an integer. We prove that for almost all partitions of an inte...
After the proof of Zhang about the existence of infinitely many bounded gaps between consecutive pri...
AbstractIf A is a set of positive integers, we denote by p(A,n) the number of partitions of n with p...
13 pagesIt is proved that the summands of almost all unequal partitions of $n$ are well-distributed ...
AbstractThe expressions ϕ(n)+σ(n)−3n and ϕ(n)+σ(n)−4n are unusual among linear combinations of arith...
AbstractRamanujanʼs famous partition congruences modulo powers of 5, 7, and 11 imply that certain se...
AbstractUsing elementary methods, we establish several new Ramanujan type identities and congruences...
This paper shows how to prove the Theorem = , i.e., the number of partitions of n into p-parts is e...
AbstractWe provide some further theorems on the partitions generated by the rank parity function. Ne...
International audienceImproving on some results of J.-L. Nicolas, the elements of the set ${\cal A}=...
International audienceImproving on some results of J.-L. Nicolas, the elements of the set ${\cal A}=...
International audienceImproving on some results of J.-L. Nicolas, the elements of the set ${\cal A}=...
International audienceImproving on some results of J.-L. Nicolas, the elements of the set ${\cal A}=...
12 pagesLet $d\ge 2$ be a fixed integer. We prove that a positive proportion of partitions of an int...
AbstractA new expansion is given for partial sums of Eulerʼs pentagonal number series. As a corollar...
International audienceLet $d\ge 2$ be an integer. We prove that for almost all partitions of an inte...
After the proof of Zhang about the existence of infinitely many bounded gaps between consecutive pri...
AbstractIf A is a set of positive integers, we denote by p(A,n) the number of partitions of n with p...
13 pagesIt is proved that the summands of almost all unequal partitions of $n$ are well-distributed ...
AbstractThe expressions ϕ(n)+σ(n)−3n and ϕ(n)+σ(n)−4n are unusual among linear combinations of arith...
AbstractRamanujanʼs famous partition congruences modulo powers of 5, 7, and 11 imply that certain se...
AbstractUsing elementary methods, we establish several new Ramanujan type identities and congruences...
This paper shows how to prove the Theorem = , i.e., the number of partitions of n into p-parts is e...