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Displaying 321 – 340 of 966

Incidence structures and closure spaces

František Machala, Vladimír Slezák (1997)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Incidence structures of independent sets

František Machala (1999)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Incidence structures of type $(p, n)$

František Machala (2003)

Czechoslovak Mathematical Journal

Every incidence structure $𝒥$ (understood as a triple of sets $(G, M, I)$ , $I \subseteq G \times M$ ) admits for every positive integer $p$ an incidence structure $𝒥^{p} = (G^{p}, M^{p}, I^{p})$ where $G^{p}$ ( $M^{p}$ ) consists of all independent $p$ -element subsets in $G$ ( $M$ ) and $I^{p}$ is determined by some bijections. In the paper such incidence structures $𝒥$ are investigated the $𝒥^{p}$ ’s of which have their incidence graphs of the simple join form. Some concrete illustrations are included with small sets $G$ and $M$ .

Independent axiom systems for nearlattices

João Araújo, Michael Kinyon (2011)

Czechoslovak Mathematical Journal

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 $2$ -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

Ivan Chajda (1995)

Archivum Mathematicum

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 $L$ 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

Radomír Halaš, Ivan Chajda (1995)

Mathematica Slovaca

Induced pseudoorders

Ivan Chajda, Miroslav Haviar (1991)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Inequalities involving $Γ$ -functionals and semi complete lattice homomorphisms

Szymon Dolecki, Maria-Pia Moschen (1987)

Rendiconti del Seminario Matematico della Università di Padova

Integer partitions, tilings of $2 D$ -gons and lattices

Matthieu Latapy (2002)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

In this paper, we study two kinds of combinatorial objects, generalized integer partitions and tilings of $2 D$ -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 $2 D$ -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

Matthieu Latapy (2010)

RAIRO - Theoretical Informatics and Applications

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.