Permutations avoiding arithmetic patterns.
Permutations et partitions : tableaux à marges égales et distance partitionnelle
Permutations of the natural numbers with prescribed difference multisets.
Permutations preserving Cesàro mean, densities of natural numbers and uniform distribution of sequences
We are interested in permutations preserving certain distribution properties of sequences. In particular we consider -uniformly distributed sequences on a compact metric space , 0-1 sequences with densities, and Cesàro summable bounded sequences. It is shown that the maximal subgroups, respectively subsemigroups, of leaving any of the above spaces invariant coincide. A subgroup of these permutation groups, which can be determined explicitly, is the Lévy group . We show that is big in the...
Permutations with coefficients in a subfield
Permutations with inversions.
Permuting the partitions of a prime
Given an odd prime number , we characterize the partitions of with non negative parts for which there exist permutations of the set such that divides but does not divide . This happens if and only if the maximal number of equal parts of is less than . The question appeared when dealing with sums of -th powers of resolvents, in order to solve a Galois module structure problem.
Petites solutions des congruences
Petits discriminants
Petits discriminants
On construit des corps de nombres de petits discriminants relativement aux minorations de Odlyzko.
Petits zéros de fonctions L de formes modulaires
Pfaffians, central simple algebras and similtudes.
Pfaffien et discriminant
Pfister Ideals in Witt Rings.
Pfister's conjecture on quadratic Co-fields.
Pfister's Dimension and the Level of Fields.
Piatetski-Shapiro meets Chebotarev
Let K be a finite Galois extension of the field ℚ of rational numbers. We prove an asymptotic formula for the number of Piatetski-Shapiro primes not exceeding a given quantity for which the associated Frobenius class of automorphisms coincides with any given conjugacy class in the Galois group of K/ℚ. In particular, this shows that there are infinitely many Piatetski-Shapiro primes of the form a² + nb² for any given natural number n.
Piatetski-Shapiro sequences
Piatetski-Shapiro sequences via Beatty sequences
Integer sequences of the form , where 1 < c < 2, can be locally approximated by sequences of the form ⌊nα+β⌋ in a very good way. Following this approach, we are led to an estimate of the difference , which measures the deviation of the mean value of φ on the subsequence from the expected value, by an expression involving exponential sums. As an application we prove that for 1 < c ≤ 1.42 the subsequence of the Thue-Morse sequence indexed by attains both of its values with asymptotic...
Picard groups of Witt rings.