Ideal systems and lattice theory.
Ideal theory in commutative semigroups.
Ideals in distributive posets
We prove that any ideal in a distributive (relative to a certain completion) poset is an intersection of prime ideals. Besides that, we give a characterization of n-normal meet semilattices with zero, thus generalizing a known result for lattices with zero.
Ideals of binary relational systems
Idéaux et congruences dans un treillis
Implications partielles dans un contexte
Nous présentons une extension de la théorie des implications entre attributs binaires aux implications partielles. A partir de données expérimentales on s'intéresse non seulement aux implications (globales), mais aussi aux «implications avec quelques contre exemples». Les implications partielles offrent une possibilité d'extraire des informations supplémentaires. Elles permettent de «modéliser» la fréquence relative d'une implication, non-valide pour toutes les données, et donnent par conséquent...
Incidence structures and closure spaces
Incidence structures of independent sets
Incidence structures of type
Every incidence structure (understood as a triple of sets , ) admits for every positive integer an incidence structure where () consists of all independent -element subsets in () and is determined by some bijections. In the paper such incidence structures are investigated the ’s of which have their incidence graphs of the simple join form. Some concrete illustrations are included with small sets and .
Independent axiom systems for nearlattices
A nearlattice is a join semilattice such that every principal filter is a lattice with respect to the induced order. Hickman and later Chajda et al independently showed that nearlattices can be treated as varieties of algebras with a ternary operation satisfying certain axioms. Our main result is that the variety of nearlattices is -based, and we exhibit an explicit system of two independent identities. We also show that the original axiom systems of Hickman as well as that of Chajda et al are...
Indexed annihilators in lattices
The concept of annihilator in lattice was introduced by M. Mandelker. Although annihilators have some properties common with ideals, the set of all annihilators in need not be a lattice. We give the concept of indexed annihilator which generalizes it and we show the basic properties of the lattice of indexed annihilators. Moreover, distributive and modular lattices can be characterized by using of indexed annihilators.
Indexed annihilators in ordered sets
Induced pseudoorders
Inequalities involving -functionals and semi complete lattice homomorphisms
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.
Intersection Graphs of Lattices
Intersection Graphs of Semilattices
Intervals, convex sublattices and subdirect representations of lattices
Intrinsic topologies on semilattices of finite breadth.