Inverse zero-sum problems and algebraic invariants
Inverse zero-sum problems {II}
Inverse zero-sum problems {III}
Inverse zero-sum problems in finite Abelian p-groups
We study the minimal number of elements of maximal order occurring in a zero-sumfree sequence over a finite Abelian p-group. For this purpose, and in the general context of finite Abelian groups, we introduce a new number, for which lower and upper bounds are proved in the case of finite Abelian p-groups. Among other consequences, our method implies that, if we denote by exp(G) the exponent of the finite Abelian p-group G considered, every zero-sumfree sequence S with maximal possible length over...
Inversion of generating functions using determinants.
-functions of automorphic forms and combinatorics: Dyck paths
We give a combinatorial interpretation for the positive moments of the values at the edge of the critical strip of the -functions of modular forms of and . We deduce some results about the asymptotics of these moments. We extend this interpretation to the moments twisted by the eigenvalues of Hecke operators.
Lattices in ℤ² and the congruence xy+uv ≡ c(mod m)
Logarithmic density of a sequence of integers and density of its ratio set
In the paper sufficient conditions for the -density of a set of positive integers in terms of logarithmic densities are given. They differ substantially from those derived previously in terms of asymptotic densities.
Maximal sets of numbers not containing k+1 pairwise coprime integers
Measures of sum-free intersecting families.
Minimal zero sequences of finite cyclic groups.
Minimal zero-sum sequences of maximum length in the group .
Minimum sum and difference covers of abelian groups.
Monochromatic and zero-sum sets of nondecreasing modified diameter.
Multiple convolution formulae on classical combinatorial numbers.
Multiple tilings of with long periods, and tiles with many-generated level semigroups.
Negative values of cosine sums
Non-degenerate Hilbert cubes in random sets
A slight modification of the proof of Szemerédi’s cube lemma gives that if a set satisfies , then must contain a non-degenerate Hilbert cube of dimension . In this paper we prove that in a random set determined by for , the maximal dimension of non-degenerate Hilbert cubes is a.e. nearly and determine the threshold function for a non-degenerate -cube.
Note on a problem of Ruzsa
Number of representations related to a linear recurrent basis