Writing the second edition of this text was a wonderful opportunity for a more mature
presentation than I was able to give 13 years ago. The intent still is to give a self-contained …

Lattice theory evolved as part of algebra in the nineteenth century through the work of Boole,
Peirce and Schröder, and in the first half of the twentieth century through the work of …

Let be a finite set. A family of subsets of is called a convex geometry with ground set if (1);(2)
whenever; and (3) if and, there is an element such that. As a nonempty family of sets, a …

Abstract Closure systems C⊂ 2 M on a finite set M arise in many areas of discrete
mathematics. They are conveniently encoded by either the family Irr (C) of meet irreducible …

Motivated by generalizing Khovanov's categorification of the Jones polynomial, we study
functors $ F $ from thin posets $ P $ to abelian categories $\mathcal {A} $. Such functors $ F …

Decomposing the hypercube Qn into n isomorphic edge-disjoint trees - ScienceDirect Skip to
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We study a dependence relation between the join-irreducible elements of a finite lattice that
generalizes the classical perspectivity relation between the atoms of a geometric lattice. This …

In this paper we extensively treat the following problems: When is a given graph a subgraph
(resp. induced subgraph) of a hypercube and when is an ordered set a subdiagram (resp …

A Boolean layer cake is an ordered set obtained from a Boolean lattice 2n by selecting any
number of complete level sets from 2n and endowing their set union with the order inherited …

The dualization in arbitrary posets is a well-studied problem in combinatorial enumeration
and is a crucial step in many applications in logics, databases, artificial intelligence and …