On relations
On representation of cyclically ordered sets
On semimodular lattices of generating systems
On some hypotheses concerning trees.
On Some Intercalations In Ordered Sets
On some minimal problem
On some partial orders associated to generic initial ideals.
On some topologies on products of ordered sets
On sums over partially ordered sets.
On system of subobject functors in the category of ordered sets
On systems of overlapping sets and symmetric polynomial inequalities
On Tabor's problem concerning a certain quasi-ordering of iterative roots of functions.
On ternary semigroups of homomorphisms of ordered sets
The paper deals with the characterization of ordered sets by means of ternary semigroups of homomorphisms of ordered sets.
On the automorphism group of the countable dense circular order
Let (C,R) be the countable dense circular ordering, and G its automorphism group. It is shown that certain properties of group elements are first order definable in G, and these results are used to reconstruct C inside G, and to demonstrate that its outer automorphism group has order 2. Similar statements hold for the completion C̅.
On the “Bruhat graph” of a Coxeter system
On the cancellation law for disconnected partially ordered sets
On the characterization of semilattices satisfying the descending chain condition and some remarks on distinguishing subsets
On the closed left ideals of the group algebra
On the combinatorics of Kac's asymmetry function
We use categories to recast the combinatorial theory of full heaps, which are certain labelled partially ordered sets that we introduced in previous work. This gives rise to a far simpler set of definitions, which we use to outline a combinatorial construction of the so-called loop algebras associated to affine untwisted Kac--Moody algebras. The finite convex subsets of full heaps are equipped with a statistic called parity, and this naturally gives rise to Kac's asymmetry function. The latter is...
On the compactification of closure algebras