Relational Concept Analysis (RCA) is a useful tool for classi cation and rule discovery on sets of objects with relations. Based on FCA, it produces more results than the latter but also an increase in complexity. Besides, in numerous applications of FCA, AOC-posets are used rather than lattices in order to reduce combinatorial problems. An AOC-poset is a subset of the concept lattice consideri...

We define toric partial orders, corresponding to regions of graphic toric hyperplane arrangements, just as ordinary partial orders correspond to regions of graphic hyperplane arrangements. Combinatorially, toric posets correspond to finite posets under the equivalence relation generated by converting minimal elements into maximal elements, or sources into sinks. We derive toric analogues for se...

We refine a technique used in a paper by Schur on real-rooted polynomials. This amounts to an extension of a theorem of Wagner on Hadamard products of Pólya frequency sequences. We also apply our results to polynomials for which the Neggers-Stanley Conjecture is known to hold. More precisely, we settle interlacing properties for E-polynomials of series-parallel posets and column-strict labelled...

An Alexandroff space is a topological in which every intersection of open sets open. There one to correspondence between T0 -spaces and partially ordered (posets). We investigate -topologies on finite quandles. prove that there non-trivial topology quandle making right multiplications continuous functions if only the has more than orbit. Furthermore, we show posets quandles with n orbits are n-...

This paper studies the poset of eigenspaces of elements of an imprimitive unitary reflection group, for a fixed eigenvalue, ordered by the reverse of inclusion. The study of this poset is suggested by the eigenspace theory of Springer and Lehrer. The posets are shown to be isomorphic to certain subposets of Dowling lattices (the ”d-divisible, k-evenly coloured Dowling lattices”). This enables u...

It is proved that the critical cells of a discrete Morse function in the sense of Forman on a finite regular CW complex can always be detected by a polyhedral Morse function in the sense of Banchoff on an appropriate embedding in Euclidean space of the barycentric subdivision of the complex. The proof is stated in terms of discrete Morse functions on a class of posets that is slightly broader t...

In this article, we characterise all continuous posets which are partially metrizable in their Scott topology. We present conditions for pmetrizability, which are both necessary and sufficient, in terms of measurements, domain-theoretic bases and, in a more general setting, in terms of radially convex metrics. These conditions, together with their refinements and generalisations, set a natural ...

A brief introduction to the theory of ordered sets and lattice theory is given. To illustrate proof techniques in the theory of ordered sets, a generalization of a conjecture of Daykin and Daykin, concerning the structure of posets that can be partitioned into chains in a \strong" way, is proved. The result is motivated by a conjecture of Graham's concerning probability correlation inequalities...

We show that for two quivers without oriented cycles related by a BGP reflection, the posets of their cluster tilting objects are related by a simple combinatorial construction, which we call a flip-flop. We deduce that the posets of cluster tilting objects of derived equivalent path algebras of quivers without oriented cycles are universally derived equivalent. In particular, all Cambrian latt...