Identically distributed pairs of partition statistics.
Improvement on Davenport's iterative method and new results in additive number theory III
Improvement on Davenport's iterative method and new results in additive number theory, I
Improvement on Davenport's iterative method and new results in additive number theory II. Proof that G(5)≤22
Increasing integer sequences and Goldbach's conjecture
Increasing integer sequences include many instances of interesting sequences and combinatorial structures, ranging from tournaments to addition chains, from permutations to sequences having the Goldbach property that any integer greater than 1 can be obtained as the sum of two elements in the sequence. The paper introduces and compares several of these classes of sequences, discussing recurrence relations, enumerative problems and questions concerning shortest sequences.
Indecomposable tilings of the integers with exponentially long periods.
Infinite families of divisibility properties modulo 4 for non-squashing partitions into distinct parts.
Infinite products over hyperpyramid lattices.
Infinite products over visible lattice points.
Integer partitions and convexity.
Integer partitions into arithmetic progressions with an odd common difference.
Integer partitions, tilings of -gons and lattices
In this paper, we study two kinds of combinatorial objects, generalized integer partitions and tilings of -gons (hexagons, octagons, decagons, etc.). We show that the sets of partitions, ordered with a simple dynamics, have the distributive lattice structure. Likewise, we show that the set of tilings of a -gon is the disjoint union of distributive lattices which we describe. We also discuss the special case of linear integer partitions, for which other dynamical models exist.
Integer Partitions, Tilings of 2D-gons and Lattices
In this paper, we study two kinds of combinatorial objects, generalized integer partitions and tilings of 2D-gons (hexagons, octagons, decagons, etc.). We show that the sets of partitions, ordered with a simple dynamics, have the distributive lattice structure. Likewise, we show that the set of tilings of a 2D-gon is the disjoint union of distributive lattices which we describe. We also discuss the special case of linear integer partitions, for which other dynamical models exist.
Integer partitions with fixed subsums.
Integer Points Close to a Smooth Curve
∗ This research is partially supported by the Bulgarian National Science Fund under contract MM-403/9We review the existing estimates for the number of integer points close to a smooth curve and improve on some of these.
Integer points close to convex hypersurfaces
Integer points close to convex surfaces
Integer Points on Curves and Surfaces.
Integers not of the form
Intersective sets given by a polynomial