Related papers: An (almost) optimal answer to a question by Wilf

We propose several techniques to construct complete permutation polynomials of finite fields by virtue of complete permutations of subfields. In some special cases, any complete permutation polynomials over a finite field can be used to…

Huayi Chen introduces the notion of an approximable graded algebra, which he uses to prove a Fujita-type theorem in the arithmetic setting, and asked if any such algebra is the graded ring of a big line bundle on a projective variety. This…

We survey the theory of increasing and decreasing subsequences of permutations. Enumeration problems in this area are closely related to the RSK algorithm. The asymptotic behavior of the expected value of the length is(w) of the longest…

Given an alphabet $S$, we consider the size of the subsets of the full sequence space $S^{\rm {\bf Z}}$ determined by the additional restriction that $x_i\not=x_{i+f(n)},\ i\in {\rm {\bf Z}},\ n\in {\rm {\bf N}}.$ Here $f$ is a positive,…

Permutation polynomials are an interesting subject of mathematics and have applications in other areas of mathematics and engineering. In this paper, we develop general theorems on permutation polynomials over finite fields. As a…

The research on pattern-avoidance has yielded so far limited knowledge on Wilf-ordering of permutations. The Stanley-Wilf limits sqrt[n](|S_n(tau)|) and further works suggest asymptotic ordering of layered versus monotone patterns. Yet,…

The rate of convergence of the distribution of the length of the longest increasing subsequence, toward the maximal eigenvalue of certain matrix ensembles, is investigated. For finite-alphabet uniform and nonuniform i.i.d. sources, a rate…

We provide a geometric condition that guarantees strong Wilf equivalence in the generalized factor order. This provides a powerful tool for proving specific and general Wilf equivalence results, and several such examples are given.

We determine the maximal pseudovarieties of finite semigroups that satisfy an identity of the form $x_1 \dots x_n \approx \rho(x_1, \dots, x_n)$. Applying this classification, we further show that a pseudovariety of permutative semigroups…

Let $A$ be a subset of primes up to $x$. If we assume $A$ is well-distributed (in the Siegel-Walfisz sense) in any arithmetic progressions to moduli $q\leqslant(\log x)^c$ for any $c>0$, then the sumset $A+A$ has density 1/2 in the natural…

This paper deals with properties of the algebraic variety defined as the set of zeros of a "deficient" sequence of multivariate polynomials. We consider two types of varieties: ideal-theoretic complete intersections and absolutely…

We prove almost sure convergence of the maximum degree in an evolving graph model combining a growing number of local choices with sublinear preferential attachment. At each step in the growth of the graph, a new vertex is introduced. Then…

We study a class of overdetermined algebraic systems of equations. We prove that the number of distinct solutions equals to the maximal possible if and only if certain matrices are commuting and semisimple. This gives a characterization of…

We construct a refined bijection $\phi$ between alternating permutations and 0-1-2 increasing trees with degree at most 2. It satisfies that the first element of alternating permutation $\pi$ is equal to the first vertex in $\phi(\pi)$ in…

We establish a phase transition for permutation classes (downsets of permutations under the permutation containment order): there is an algebraic number $\kappa$, approximately 2.20557, for which there are only countably many permutation…

We present an algorithm running in time O(n ln n) which decides if a wreath-closed permutation class Av(B) given by its finite basis B contains a finite number of simple permutations. The method we use is based on an article of Brignall,…

We prove necessary and sufficient conditions on a family of (generalised) gridding matrices to determine when the corresponding permutation classes are partially well-ordered. One direction requires an application of Higman's Theorem and…

We consider almost-primes of the form $f(p)$ where $f$ is an irreducible polynomial over $\mathbb Z$ and $p$ runs over primes. We improve a result of Richert for polynomials of degree at least $3$. In particular we show that, when the…

We consider the number of passes a permutation needs to take through a stack if we only pop the appropriate output values and start over with the remaining entries in their original order. We define a permutation $\pi$ to be $k$-pass…

Let $f \colon X \to Y$ be a morphism of concentrated schemes. We characterize $f$-perfect complexes $\mathcal{E}$ as those such that the functor $\mathcal{E} \otimes^{\mathbf{L}}_X \mathbf{L} f^*-$ preserves bounded complexes. We prove, as…