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Displaying 581 – 600 of 995

On the jump number of lexicographic sums of ordered sets

Hyung Chan Jung, Jeh Gwon Lee (2003)

Czechoslovak Mathematical Journal

Let $Q$ be the lexicographic sum of finite ordered sets $Q_{x}$ over a finite ordered set $P$ . For some $P$ we can give a formula for the jump number of $Q$ in terms of the jump numbers of $Q_{x}$ and $P$ , that is, $s (Q) = s (P) + \sum_{x \in P} s (Q_{x})$ , where $s (X)$ denotes the jump number of an ordered set $X$ . We first show that $w (P) - 1 + \sum_{x \in P} s (Q_{x}) \leq s (Q) \leq s (P) + \sum_{x \in P} s (Q_{x})$ , where $w (X)$ denotes the width of an ordered set $X$ . Consequently, if $P$ is a Dilworth ordered set, that is, $s (P) = w (P) - 1$ , then the formula holds. We also show that it holds again if $P$ is bipartite. Finally, we prove that the lexicographic sum of...

On the lattice of pronormal subgroups of dicyclic, alternating and symmetric groups

Shrawani Mitkari, Vilas Kharat (2024)

Mathematica Bohemica

In this paper, the structures of collection of pronormal subgroups of dicyclic, symmetric and alternating groups $G$ are studied in respect of formation of lattices $L (G)$ and sublattices of $L (G)$ . It is proved that the collections of all pronormal subgroups of $A_{n}$ and S $_{n}$ do not form sublattices of respective $L (A_{n})$ and $L (S_{n})$ , whereas the collection of all pronormal subgroups $LPrN ({Dic}_{n})$ of a dicyclic group is a sublattice of $L ({Dic}_{n})$ . Furthermore, it is shown that $L ({Dic}_{n})$ and $LPrN ({Dic}_{n}$ ) are lower semimodular lattices.

On the lattices of kernels of isotonic mappings. II

Teo Sturm (1977)

Czechoslovak Mathematical Journal

On the Livingstone-Wagner theorem.

Mnukhin, V.B., Siemons, I.J. (2004)

The Electronic Journal of Combinatorics [electronic only]

On the modularity of the lattice of fundamental orders on a semilattice.

S.M. Goberstein (1982)

Semigroup forum

On the number of distributive lattices.

Erné, Marcel, Heitzig, Jobst, Reinhold, Jürgen (2002)

The Electronic Journal of Combinatorics [electronic only]

On the number of finite algebraic structures

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

Journal of the European Mathematical Society

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 with few...

On the Order Type L-valued Relations on L-powersets.

I. Uljane (2007)

Mathware and Soft Computing

On the power of ordered sets

Milan Sekanina (1965)

Archivum Mathematicum

On the powers of Voiculescu's circular element

Ferenc Oravecz (2001)

Studia Mathematica

The main result of the paper is that for a circular element c in a C*-probability space, $(c ⁿ, c^{n *})$ is an R-diagonal pair in the sense of Nica and Speicher for every n = 1,2,... The coefficients of the R-series are found to be the generalized Catalan numbers of parameter n-1.

On the pullback stability of a quotient map with respect to a closure operator.

Sousa, Lurdes (2001)

Theory and Applications of Categories [electronic only]

On the relation between heterogeneous uniform 2-algebraic closure operators and heterogeneous algebras.

Joan B. Climent, Luis Fernandino Larrinaga (1989)

Collectanea Mathematica

On the representation of orthocomplemented posets

František Katrnoška (1982)

Commentationes Mathematicae Universitatis Carolinae

On the semigroup of closure operations.

S.V. Tolstosheina (1990)

Semigroup forum

On the structure of semilattice sums

Anna B. Romanowska, Jonathan D. H. Smith (1991)

Czechoslovak Mathematical Journal

On the subsemilattices of first-order definable and openly first-order definable congruences of the congruence lattice of a universal algebra.

Pinus, A.G. (2006)

Sibirskij Matematicheskij Zhurnal

On the system of all maximal chains (antichains) of a graph.

D. Kurepa (1976)

Publications de l'Institut Mathématique [Elektronische Ressource]

On the tolerance extension property

Ivan Chajda (1978)

Časopis pro pěstování matematiky

On unique factorization semilattices

Pedro V. Silva (2000)

Discussiones Mathematicae - General Algebra and Applications

The class of unique factorization semilattices (UFSs) contains important examples of semilattices such as free semilattices and the semilattices of idempotents of free inverse monoids. Their structural properties allow an efficient study, among other things, of their principal ideals. A general construction of UFSs from arbitrary posets is presented and some categorical properties are derived. The problem of embedding arbitrary semilattices into UFSs is considered and complete characterizations...

On valuation in semilattices

P. V. Ramana Murty, Teresa Engelbert (1985)

Mathématiques et Sciences Humaines

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