Related papers: When all Permutations are Combinatorial Similariti…

In this note we prove a selection of commutativity theorems for various classes of semigroups. For instance, if in a separative or completely regular semigroup $S$ we have $x^p y^p = y^p x^p$ and $x^q y^q = y^q x^q$ for all $x,y\in S$ where…

After a brief review of existing results on permutation binomials of finite fields, we introduce the notion of equivalence among permutation binomials (PBs) and describe how to bring a PB to its canonical form under equivalence. We then…

A simple permutation is one which maps no proper non-singleton interval onto an interval. We consider the enumeration of simple permutations from several aspects. Our results include a straightforward relationship between the ordinary…

A criterion of joint ergodicity of several sequences of transformations of a probability measure space $X$ of the form $T_{i}^{\phi_{i}(n)}$ is given for the case where $T_{i}$ are commuting measure preserving transformations of $X$ and…

In this note we show that pattern matching in permutations is polynomial time reducible to pattern matching in set partitions. In particular, pattern matching in set partitions is NP-Complete.

If F is a type-definable family of commensurable subsets, subgroups or sub-vector spaces in a metric structure, then there is an invariant subset, subgroup or sub-vector space commensurable with F. This in particular applies to…

A semiprime is a natural number which can be written as the product of two primes. The asymptotic behaviour of the function $\pi_2(x)$, the number of semiprimes less than or equal to $x$, is studied. Using a combinatorial argument,…

Motivated by the quest for a broader understanding of communication complexity of simple functions, we introduce the class of "permutation-invariant" functions. A partial function $f:\{0,1\}^n \times \{0,1\}^n\to \{0,1,?\}$ is…

We prove that every isometry between two combinatorial spaces is determined by a permutation of the canonical unit basis combined with a change of signs. As a consequence, we show that in the case of Schreier spaces, all the isometries are…

Given a real number beta>1, a permutation pi of length n is realized by the beta-shift if there is some x in [0,1] such that the relative order of the sequence x,f(x),...,f^{n-1}(x), where f(x) is the factional part of beta*x, is the same…

The set $G$ of all $m$-dimensional subspaces of a $2m$-dimensional vector space $V$ is endowed with two relations, complementarity and adjacency. We consider bijections from $G$ onto $G'$, where $G'$ arises from a $2m'$-dimensional vector…

We consider extensions of quasiconformal maps and the uniformization theorem to the setting of metric spaces $X$ homeomorphic to $\mathbb R^2$. Given a measure $\mu$ on such a space, we introduce $\mu$-quasiconformal maps $f:X \to \mathbb…

Let H and K be two Hilbert spaces and B(H) be the algebra of all bounded linear operators from H into itself. The main purpose of this paper is to obtain a characterization of bijective maps $\Phi$ : B(H) $\rightarrow$ B(K) satisfying the…

Let $G$ be a graph with vertex set $V(G)$, $f$ a permutation of $V(G)$. Define $\delta_f(G)=|d(x,y)-d(f(x),f(y))|$ and $\delta_f(G)=\Sigma\delta_f(x,y)$, where the sum is taken over all unordered pair $x$, $y$ of distinct vertices of $G$.…

Let $G$ be a group, $\mathcal{P}_G$ be the family of all subsets of $G$. For a subset $A\subseteq G$, we put $\Delta(A)=\{g\in G:|gA\cap A|=\infty\}$. The mapping $\Delta:\mathcal{P}_G\rightarrow\mathcal{P}_G$, $A\mapsto\Delta(A)$, is…

A \emph{self-complementary} graph is a graph isomorphic to its complement. An isomorphism between $G$ and its complement, viewed as a permutation of $V(G)$, is then called an \emph{antimorphism}. A \emph{skew partition} of $G$ is a…

In a recent paper Zheng et al. characterized the coefficients of $ f(x) = x + a_1x^{s_1(2m-1)+1} + a_2x^{s_2(2m-1)+1} + a_3x^{s_3(2m-1)+1} $ over $\mathbb{ F}_2^{2m}$ that lead $ f(x) $ to be a permutation of $\mathbb{ F}_2^{2m}$ for $…

For a map f: X -> Y of quasi-compact quasi-separated schemes, we discuss quasi-perfection, that is, the right adjoint f^\times of the derived functor Rf_* respects small direct sums. This is equivalent to the existence of a functorial…

We show that every quasitrivial n-ary semigroup is reducible to a binary semigroup, and we provide necessary and sufficient conditions for such a reduction to be unique. These results are then refined in the case of symmetric n-ary…

The symmetric function theorem states that a polynomial that is invariant under permutation of variables, is a polynomial in the elementary symmetric polynomials. We deduce this classical result, in the analytic setting, from the…