Unimodal (i.e. single-humped) permutations may be decomposed into a product of disjoint cycles. Some enumerative results concerning their cyclic structure — e.g. 23 of them contain fixed points — are given. We also obtain in effect a kind of combinatorial universality for continuous unimodal maps, by severely constraining the possible ways periodic orbits of any such map can nestle together. Bu...

Abstract. We construct a discrete model of the homotopy theory of S-spaces. We define a category P with objects composed of a simplicial set and a cyclic set along with suitable compatibility data. P inherits a model structure from the model structures on the categories of simplicial sets and cyclic sets. We then show that there is a Quillen equivalence between P and the model category of S-spa...

A description is given of finite permutation groups containing a cyclic regular subgroup. It is then applied to derive a classification of arc transitive circulants, completing the work dating from 1970’s. It is shown that a connected arc transitive circulant of order n is one of the following: a complete graph Kn , a lexicographic product [K̄b], a deleted lexicographic product [K̄b] − b , where ...

A covalence sequence of a vertex-transitive map is a cyclic sequence of covalences around a vertex of the map. We explain the algebraic background for a study of the relationship between covalence sequences of maps on compact orientable surfaces and covalence sequences of (infinite) plane tessellations that both exhibit the same ‘level of transitivity’ of automorphism groups on vertices or edges.

Let G = Z4. We construct examples of G-equivariant entire rational maps from non-singular real algebraic G-varieties to Grassmannians with appropriate actions of G. These examples of strongly algebraicZ4 vector bundles facilitate a key step in the verification of Conjecture1.1 in the general cyclic group action case.

We construct a new class of positive indecomposable maps in the algebra of d × d complex matrices. Each map is uniquely characterized by a cyclic bistochastic matrix. This class generalizes a Choi map for d = 3. It provides a new reach family of indecomposable entanglement witnesses which define important tool for investigating quantum entanglement.

Two enzymes displaying cyclic GMP-stimulated cyclic AMP phosphodiesterase activity were purified from rat liver to apparent homogeneity: a 'particulate enzyme' found as an integral membrane protein associated with the plasma membrane, and a 'soluble' enzyme found in the cytosol. The physical properties of these enzymes were very similar, being dimers of Mr 134,000, composed in each instance of ...

In this paper, properties of reflexible Cayley maps for abelian groups are investigated, and as a result, it is shown that a regular Cayley map of valency greater than 2 for a cyclic group is reflexible if and only if it is anti-balanced.

The intent of the paper is to study semi-cyclic type contraction condition for a pair of maps (S, T). Our aim is to establish an existence theorem for common fixed points and best proximity points for such a pair in Banach spaces. The results obtained herein extend some recent results.

In this paper we generalize Kaplansky's combinatorial characterization of the isomorphism types embeddings a cyclic subgroup in finite abelian group given his 1951 book ``Infinite Abelian Groups''. For introduce partial maps on Littlewood-Richardson tableaux and show that they characterize direct sums such embeddings.