On the definition of a Lachlan semilattice.
On the dimension of finite permutation group actions.
On the dominance partial ordering of Dyck paths.
On The Essential Flats Of Geometric Lattices
On the essential of geometric lattices.
On the height of order ideals
We maximize the total height of order ideals in direct products of finitely many finite chains. We also consider several order ideals simultaneously. As a corollary, a shifting property of some integer sequences, including digit sum sequences, is derived.
On the jump number of lexicographic sums of ordered sets
Let be the lexicographic sum of finite ordered sets over a finite ordered set . For some we can give a formula for the jump number of in terms of the jump numbers of and , that is, , where denotes the jump number of an ordered set . We first show that , where denotes the width of an ordered set . Consequently, if is a Dilworth ordered set, that is, , then the formula holds. We also show that it holds again if is bipartite. Finally, we prove that the lexicographic sum of...
On the lattice of pronormal subgroups of dicyclic, alternating and symmetric groups
In this paper, the structures of collection of pronormal subgroups of dicyclic, symmetric and alternating groups are studied in respect of formation of lattices and sublattices of . It is proved that the collections of all pronormal subgroups of and S do not form sublattices of respective and , whereas the collection of all pronormal subgroups of a dicyclic group is a sublattice of . Furthermore, it is shown that and ) are lower semimodular lattices.
On the lattices of kernels of isotonic mappings. II
On the Livingstone-Wagner theorem.
On the modularity of the lattice of fundamental orders on a semilattice.
On the number of distributive lattices.
On the number of finite algebraic structures
We prove that every clone of operations on a finite set , if it contains a Malcev operation, is finitely related – i.e., identical with the clone of all operations respecting for some finitary relation over . It follows that for a fixed finite set , 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.
On the power of ordered sets
On the powers of Voiculescu's circular element
The main result of the paper is that for a circular element c in a C*-probability space, 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.
On the relation between heterogeneous uniform 2-algebraic closure operators and heterogeneous algebras.
On the representation of orthocomplemented posets
On the semigroup of closure operations.