Honeycomb arrays.
Hrátky s geometrií, čísly a maticemi
Hyperbolic and Parabolic Packings.
Hyperplane Arrangements with a Lattice of Regions.
Hyperplane Coverings and Blocking Sets.
Hyperplanes in matroids and the axiom of choice
We show that in set theory without the axiom of choice ZF, the statement sH: “Every proper closed subset of a finitary matroid is the intersection of hyperplanes including it” implies AC, the axiom of choice for (nonempty) finite sets. We also provide an equivalent of the statement AC in terms of “graphic” matroids. Several open questions stay open in ZF, for example: does sH imply the axiom of choice?
Il sottogruppo generato dalle involuzioni regolari di un -ovale -transitivo
Improved LP lower bounds for difference triangle sets.
Improvement of inequalities for the -structures and some geometrical connections
The main results are the inequalities (1) and (6) for the minimal number of -structure classes,which improve the ones from [3], and also some geometrical connections, especially the inequality (13).
Improving dense packings of equal disks in a square.
Incidence complexes and r-connectedness
Incomplete idempotent Schröder quasigroups and related packing designs.
Indecomposable tilings of the integers with exponentially long periods.
Independence structures in the geometry of orders.
Inequalities for t-Designs with Repeated Blocks.
Inequalities of Bonferroni-Galambos type with applications to the Tutte polynomial and the chromatic polynomial.
Inflationary tilings with a similarity structure.
Inklusions- und Abstimmungssysteme.
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.