Related papers: Pin classes II: Small pin classes

Permutation polynomials over finite fields have important applications in many areas of science and engineering such as coding theory, cryptography, combinatorial design, etc. In this paper, we construct several new classes of permutation…

A sequence of reversals that takes a signed permutation to the identity is perfect if at no step a common interval is broken. Determining a parsimonious perfect sequence of reversals that sorts a signed permutation is NP-hard. Here we show…

We prove that it is decidable if a finitely based permutation class contains infinitely many simple permutations, and establish an unavoidable substructure result for simple permutations: every sufficiently long simple permutation contains…

We study transitions between phases of matter with topological order. By studying these transitions in exactly solvable lattice models we show how universality classes may be identified and critical properties described. As a familiar…

Let V be a d-dimensional vector space over a field of prime order p. We classify the affine transformations of V of order at least p^d/4, and apply this classification to determine the finite primitive permutation groups of affine type, and…

We study first-passage percolation in two dimensions, using measures mu on passage times with b:=inf supp(mu) >0 and mu({b})=p \geq p_c, the threshold for oriented percolation. We first show that for each such mu, the boundary of the limit…

A consecutive pattern in a permutation $\pi$ is another permutation $\sigma$ determined by the relative order of a subsequence of contiguous entries of $\pi$. Traditional notions such as descents, runs and peaks can be viewed as particular…

We investigate certain classes of integrable classical or quantum spin systems. The first class is characterized by the recursively defined property $P$ saying that the spin system consists of a single spin or can be decomposed into two…

In the pseudogap regime of one-dimensional incommensurate Peierls systems, fluctuations of the phase of the order parameter prohibit the emergence of long-range order and generate a finite correlation length. For classical phase…

We define the operation of composing two hereditary classes of permutations using the standard composition of permutations as functions and we explore properties and structure of permutation classes considering this operation. We mostly…

Machines whose main purpose is to permute and sort data are studied. The sets of permutations that can arise are analysed by means of finite automata and avoided pattern techniques. Conditions are given for these sets being enumerated by…

Statistical physics can describe the behavior of microbial populations consisting of many heterogeneous individuals. A direct consequence is the existence of phase transitions, where the behavior of a population changes discontinuously upon…

For a given permutation or set partition there is a natural way to assign a genus. Counting all permutations or partitions of a fixed genus according to cycle lengths or block sizes, respectively, is the main content of this article. After…

This study proposes a new analytical model for grain boundary pinning by second phase particles in two-dimensional polycrystals. This approach not only considers how particles impede grain growth, but also elucidates their role in…

A transitive permutation group is said to be semiprimitive if each of its normal subgroups is either semiregular or transitive.The class of semiprimitive groups properly contains primitive groups, quasiprimitive groups and innately…

We consider a simple discrete-time Markov chain with values in $[0,\infty)^{Z^d}$. The Markov chain describes various interesting examples such as oriented percolation, directed polymers in random environment, time discretizations of binary…

The age of each countable homogeneous permutation forms a Ramsey class. Thus, there are five countably infinite Ramsey classes of permutations.

In the first paper in this series we estimated the probability that a random permutation $\pi\in\mathcal{S}_n$ has a fixed set of a given size. In this paper, we elaborate on the same method to estimate the probability that $\pi$ has $m$…

The finite-size scaling theory for continuous phase transition plays an important role in determining critical point and critical exponents from the size-dependent behaviors of quantities in the thermodynamic limit. For percolation phase…

A descent $k$ of a permutation $\pi=\pi_{1}\pi_{2}\dots\pi_{n}$ is called a big descent if $\pi_{k}>\pi_{k+1}+1$; denote the number of big descents of $\pi$ by $\operatorname{bdes}(\pi)$. We study the distribution of the…