On short zero-sum subsequences. II.
On some subgroup chains related to Kneser’s theorem
A recent result of Balandraud shows that for every subset of an abelian group there exists a non trivial subgroup such that holds only if . Notice that Kneser’s Theorem only gives .This strong form of Kneser’s theorem follows from some nice properties of a certain poset investigated by Balandraud. We consider an analogous poset for nonabelian groups and, by using classical tools from Additive Number Theory, extend some of the above results. In particular we obtain short proofs of Balandraud’s...
On sums of sequences of integers, I
On sum-sets and product-sets of complex numbers
We give a simple argument that for any finite set of complex numbers , the size of the the sum-set, , or the product-set, , is always large.
On the Addition of Residue Classes mod p.
On the additive completion of primes
On the bases with an exact order
On the distribution of the elliptic subset sum generator of pseudorandom numbers.
On the number of semigroups of natural numbers.
On the possible orders of a basis for a finite cyclic group.
On the postage stamp problem with the three stamp denominations.
On the postage stamp problem with three stamp denominations, III.
On the postage stamp problem with three stamp denominations, II.
On the representation of 1,2,..., n by sums
On the representation of large integers as sums of distinct summands taken from a fixed set
On the size of dissociated bases.
On the structure of sets with small doubling property on the plane (I)
Let K be a finite set of lattice points in a plane. We prove that if |K| is sufficiently large and |K+K| < (4 - 2/s)|K| - (2s-1), then there exist s - 1 parallel lines which cover K. We also obtain some more precise structure theorems for the cases s = 3 and s = 4.
On the subset sums of exponential type sequences
On the sum of dilations of a set
We show that for any relatively prime integers 1 ≤ p < q and for any finite A ⊂ ℤ one has .
On Waring's problem for squares