Combinatorial problems raised from 2-semilattices

Infinite Combinatorial Issues Raised by Lifting Problems in Universal Algebra

The critical point between varieties A and B of algebras is defined as the least cardinality of the semilattice of compact congruences of a member of A but of no member of B, if it exists. The study of critical points gives rise to a whole array of problems, often involving lifting problems of either diagrams or objects, with respect to functors. These, in turn, involve problems that belong to ...

Combinatorial problems from transformation semigroups

algebra and enumerative combinatorics We learn something when we can interpret combinatorial numbers as orders of algebraic structures, especially groups. Lagrange’s Theorem means that group orders tend to have a rich arithmetic structure. I first learned from Norman’s paper on chip-firing games the fact that the number of spanning trees of a graph is the order of an abelian group canonically a...

Problems from the Eighteenth British Combinatorial Conference

Most of these problems were presented at the problem session of the 18th British Combinatorial Conference at the University of Sussex, 2–6 July 2001. I have added some problems given to me after the session. Since two of the problems concern circular chromatic number, the entire set has a circular structure; the starting point is fixed by the sixth problem. Problem 1 (BCC18.1) Freese–Nation num...

Problems from the Nineteenth British Combinatorial Conference

Most of these problems were presented at the problem session of the 19th British Combinatorial Conference at the University College of North Wales, Bangor, 29 June–4 July 2001. I have added some problems given to me after the session. As previously, the problems are circularly ordered; you may start at any point. Problem 1 (BCC19.1) Tight single-change covering designs. Proposed by D. A. Preece...

Alcohol problems in adoptees raised apart from alcoholic biological parents.