We introduce a new algebraic construction, monop, that combines monoids (with respect to the product of species), and operads (monoids with respect to the substitution of species) in the same algebraic structure. By the use of properties of cancellative set-monops we construct a family of partially ordered sets whose prototypical examples are the Dowling lattices. They generalize the partition ...

Given an n n table of a cancellative operation on a domain of size n, we investigate the complexity of determining whether is close (equal on most pairs of inputs) to an associative, commutative, and cancellative group operation 0. We show that one can perform such a test in O(n) time. In contrast, quadratic time is necessary and sufficient to test that a given operation is cancellative, associ...

We use information theory to study recovering sets RL and strongly cancellative sets CL on different lattices. These sets are special classes of recovering pairs and cancellative sets previously discussed in the papers of Simonyi, Frankl, and Füredi. We mainly focus on the lattices Bn and D k l . Specifically, we find upper bounds and constructions for the sets RBn , CBn , and CDk l .

Z. Feng and R.W. Heath proved that any separable linearly ordered space (LOTS) which is a cancellative topological semigroup must be metrizable. In this note, we show that the same holds more generally for CCC LOTS by proving that no Souslin line admits a continuous cancellative binary operation. We also show that no Lindelöf Aronszajn line admits such an operation.

We describe a re ned superposition calculus for cancellative abelian monoids. They encompass not only abelian groups, but also such ubiquitous structures as the natural numbers or multisets. Both the AC axioms and the cancellation law are di cult for a general purpose superposition theorem prover, as they create many variants of clauses which contain sums. Our calculus requires neither explicit...

A cancellative hypergraph has no three edges A;B;C with ADBCC: We give a new short proof of an old result of Bollobás, which states that the maximum size of a cancellative triple system is achieved by the balanced complete tripartite 3-graph. One of the two forbidden subhypergraphs in a cancellative 3-graph is F5 1⁄4 fabc; abd; cdeg: For nX33 we show that the maximum number of triples on n vert...

Problems involving chains of irreducible factorizations in atomic integral domains and monoids have been the focus of much recent literature. If S is a commutative cancellative atomic monoid, then the catenary degree of S (denoted c(S)) and the tame degree of S (denoted t(S)) are combinatorial invariants of S which describe the behavior of chains of factorizations. In this note, we describe met...