Related papers: The cyclic structure of unimodal permutations
The properties of motion close to the transition of a stable family of periodic orbits to complex instability is investigated with two symplectic 4D mappings, natural extensions of the standard mapping. As for the other types of…
Mutations of the cluster variables generating the cluster algebra of type $A^{(2)}_2$ reduce to a two-dimensional discrete integrable system given by a quartic birational map. The invariant curve of the map is a singular quartic curve, and…
The existence and uniqueness of fixed points of both the cyclic self-mapping and its associate composite self-mappings on each of the subsets are investigated if the subsets in the cyclic disposal are nonempty, bounded and of nonempty…
We study the mixing properties of permutations obtained as a product of two uniformly random permutations of fixed cycle types. For instance, we give an exact formula for the probability that elements $1,2,...,k$ are in distinct cycles of…
We describe an example of a structurally stable heteroclinic network for which nearby orbits exhibit irregular but sustained switching between the various sub-cycles in the network. The mechanism for switching is the presence of spiralling…
The goal of this paper is to prove coherence results with respect to relational graphs for monoidal endofunctors, i.e. endofunctors of a monoidal category that preserve the monoidal structure up to a natural transformation that need not be…
The cyclic shift graph of a monoid is the graph whose vertices are elements of the monoid and whose edges link elements that differ by a cyclic shift. For certain monoids connected with combinatorics, such as the plactic monoid (the monoid…
Let $m, n$ be positive integers such that $m>1$ divides $n$. In this paper, we introduce a special class of piecewise-affine permutations of the finite set $[1, n]:=\{1, \ldots, n\}$ with the property that the reduction $\pmod m$ of $m$…
In aperiodic order, non-periodic but "ordered" objects such as tilings, Delone sets, functions and measures are investigated. In this article we depict the common structure of these objects by using the general framework of abstract pattern…
In an award-winning expository article, V. Pozdnyakov and J.M. Steele gave a beautiful demonstration of the ramifications of a basic bijection for permutations. The aim of this note is to connect this correspondence to a seemingly unrelated…
We investigate combinatorial dynamical systems on simplicial complexes considered as {\em finite topological spaces}. Such systems arise in a natural way from sampling dynamics and may be used to reconstruct some features of the dynamics…
We describe symmetry structure of a general singular theory (theory with constraints in the Hamiltonian formulation), and, in particular, we relate the structure of gauge transformations with the constraint structure. We show that any…
Poisson structures vanishing linearly on a set of smooth closed disjoint curves are generic in the set of all Poisson structures on a compact connected oriented surface. We construct a complete set of invariants classifying these structures…
We study the topological dynamics by iterations of a piecewise continuous, non linear and locally contractive map in a real finite dimensional compact ball. We consider those maps satisfying the "separation property": different continuity…
Problem 8.1 in Astaiza et. al. asks about the relationship between the cycle decomposition of a permutation $\sigma$ and that of its symmetric tensor power $\sigma ^{\odot k}$. In this paper, we investigate this question and give formulas…
We study the periodic cyclic homology groups of the cross-product of a finite type algebra $A$ by a discrete group $\Gamma$. In case $A$ is commutative and $\Gamma$ is finite, our results are complete and given in terms of the singular…
It is known that the suspension of a simplicial complex can be realized with only one additional point. Suitable iterations of this construction generate highly symmetric simplicial complexes with various interesting combinatorial and…
Given a transitive permutation group, a fundamental object for studying its higher transitivity properties is the permutation action of its isotropy subgroup. We reverse this relationship and introduce a universal construction of infinite…
We study countable embedding-universal and homomorphism-universal structures and unify results related to both of these notions. We show that many universal and ultrahomogeneous structures allow a concise description (called here a finite…
We consider the evolution of the unstable periodic orbit structure of coupled chaotic systems. This involves the creation of a complicated set outside of the synchronization manifold (the emergent set). We quantitatively identify a critical…