Algebraic and graph-theoretic properties of infinite $n$-posets

Zoltán Ésik; Zoltán L. Németh

Displaying similar documents to “Algebraic and graph-theoretic properties of infinite $n$ -posets”

Statisch pairs in atomistic posets

Alireza Vaezi, Vilas Kharat (2017)

Mathematica Bohemica

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We introduce statisch pairs in atomistic posets and study its relationships with some known concepts in posets such as biatomic and dual modular pairs, perspectivity and subspaces of atom space of an atomistic poset. We generalize the notion of exchange property in posets and with the help of it we prove the equivalence of dual modular, biatomic and statisch pairs in atomistic posets. Also, we prove that the set of all finite elements of a statisch poset with such property forms an ideal....

On sets related to maximal clones

Yeni Susanti, Klaus Denecke (2012)

Discussiones Mathematicae - General Algebra and Applications

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For an arbitrary h-ary relation ρ we are interested to express n-clone Polⁿρ in terms of some subsets of the set of all n-ary operations Oⁿ(A) on a finite set A, which are in general not clones but we can obtain Polⁿρ from these sets by using intersection and union. Therefore we specify the concept a function preserves a relation and moreover, we study the properties of this new concept and the connection between these sets and Polⁿρ. Particularly we study $R_{a ̲, b}^{n, k}$ for arbitrary partial order...

Direct summands of systems of continuous linear transformations

Uri Fixman, Frank A. Zorzitto

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CONTENTSIntroduction............................................................................................................ 51. The category of $C^{N}$ -systems........................................................................... 82. The problem of split monomorphisms................................................................ 103. Internal hom and tensor product........................................................................... 134. Characterizations of split monomorphisms..........................................................

Acknowledgment to the paper: “Another proof that a chain of non-empty $H$ -closed subspaces has a non-empty intersection’

J. Mioduszewski (1971)

Colloquium Mathematicae

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Ordinal remainders of classical ψ-spaces

Alan Dow, Jerry E. Vaughan (2012)

Fundamenta Mathematicae

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Let ω denote the set of natural numbers. We prove: for every mod-finite ascending chain $T_{α} : α < λ$ of infinite subsets of ω, there exists $ℳ \subset {[ω]}^{ω}$ , an infinite maximal almost disjoint family (MADF) of infinite subsets of the natural numbers, such that the Stone-Čech remainder βψ∖ψ of the associated ψ-space, ψ = ψ(ω,ℳ ), is homeomorphic to λ + 1 with the order topology. We also prove that for every λ < ⁺, where is the tower number, there exists a mod-finite ascending chain $T_{α} : α < λ$ , hence a ψ-space with...

Association schemes and MacWilliams dualities for generalized Niederreiter-Rosenbloom-Tsfasman posets

Dae San Kim, Hyun Kwang Kim

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Let P be a poset on the set [m]×[n], which is given as the disjoint sum of posets on ’columns’ of [m]×[n], and let P̌ be the dual poset of P. Then P is called a generalized Niederreiter-Rosenbloom-Tsfasman poset (gNRTp) if all further posets on columns are weak order posets of the ’same type’. Let G (resp. Ǧ) be the group of all linear automorphisms of the space $_{q}^{m \times n}$ preserving the P-weight (resp. P̌-weight). We define two partitions of $_{q}^{m \times n}$ , one consisting of ’P-orbits’ and the other of...

On $☆$ - associated comonotone functions

Ondrej Hutník, Jozef Pócs (2018)

Kybernetika

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We give a positive answer to two open problems stated by Boczek and Kaluszka in their paper [1]. The first one deals with an algebraic characterization of comonotonicity. We show that the class of binary operations solving this problem contains any strictly monotone right-continuous operation. More precisely, the comonotonicity of functions is equivalent not only to $+$ -associatedness of functions (as proved by Boczek and Kaluszka), but also to their $☆$ -associatedness with $☆$ being an arbitrary...

Regular elements and Green's relations in Menger algebras of terms

Klaus Denecke, Prakit Jampachon (2006)

Discussiones Mathematicae - General Algebra and Applications

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Defining an (n+1)-ary superposition operation $S^{n}$ on the set $W_{τ} (X_{n})$ of all n-ary terms of type τ, one obtains an algebra $n - c l o n e τ : = (W_{τ} (X_{n}); S^{n}, x_{1}, . . ., x_{n})$ of type (n+1,0,...,0). The algebra n-clone τ is free in the variety of all Menger algebras ([9]). Using the operation $S^{n}$ there are different possibilities to define binary associative operations on the set $W_{τ} (X_{n})$ and on the cartesian power $W_{τ} {(X_{n})}^{n}$ . In this paper we study idempotent and regular elements as well as Green’s relations in semigroups of terms with these binary associative...

Chromatic number of the product of graphs, graph homomorphisms, antichains and cofinal subsets of posets without AC

Amitayu Banerjee, Zalán Gyenis (2021)

Commentationes Mathematicae Universitatis Carolinae

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In set theory without the axiom of choice (AC), we observe new relations of the following statements with weak choice principles. $\circ$ If in a partially ordered set, all chains are finite and all antichains are countable, then the set is countable. $\circ$ If in a partially ordered set, all chains are finite and all antichains have size $ℵ_{α}$ , then the set has size $ℵ_{α}$ for any regular $ℵ_{α}$ . $\circ$ Every partially ordered set without a maximal element has two disjoint cofinal sub sets – CS. $\circ$ Every partially...

The induced paths in a connected graph and a ternary relation determined by them

Ladislav Nebeský (2002)

Mathematica Bohemica

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By a ternary structure we mean an ordered pair $(X_{0}, T_{0})$ , where $X_{0}$ is a finite nonempty set and $T_{0}$ is a ternary relation on $X_{0}$ . By the underlying graph of a ternary structure $(X_{0}, T_{0})$ we mean the (undirected) graph $G$ with the properties that $X_{0}$ is its vertex set and distinct vertices $u$ and $v$ of $G$ are adjacent if and only if ${x \in X_{0} T_{0} (u, x, v)} \cup {x \in X_{0} T_{0} (v, x, u)} = {u, v} .$ A ternary structure $(X_{0}, T_{0})$ is said to be the B-structure of a connected graph $G$ if $X_{0}$ is the vertex set of $G$ and the following statement holds for all $u, x, y \in X_{0}$ : $T_{0} (x, u, y)$ if and only if $u$ belongs to an...

A computation of positive one-peak posets that are Tits-sincere

Marcin Gąsiorek, Daniel Simson (2012)

Colloquium Mathematicae

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A complete list of positive Tits-sincere one-peak posets is provided by applying combinatorial algorithms and computer calculations using Maple and Python. The problem whether any square integer matrix $A \in ₙ (ℤ)$ is ℤ-congruent to its transpose $A^{t r}$ is also discussed. An affirmative answer is given for the incidence matrices $C_{I}$ and the Tits matrices $C ̂_{I}$ of positive one-peak posets I.

On the number of finite algebraic structures

Erhard Aichinger, Peter Mayr, R. McKenzie (2014)

Journal of the European Mathematical Society

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We prove that every clone of operations on a finite set $A$ , if it contains a Malcev operation, is finitely related – i.e., identical with the clone of all operations respecting $R$ for some finitary relation $R$ over $A$ . It follows that for a fixed finite set $A$ , the set of all such Malcev clones is countable. This completes the solution of a problem that was first formulated in 1980, or earlier: how many Malcev clones can finite sets support? More generally, we prove that every finite algebra...

Displaying similar documents to “Algebraic and graph-theoretic properties of infinite n -posets”

Displaying similar documents to “Algebraic and graph-theoretic properties of infinite $n$ -posets”