Let S be a subset of the positive integers, and let σ be a permutation of S. We say that σ is a k-avoiding permutation of S if σ does not contain any k-term AP as a subsequence. Similarly, the set S is said to be k-avoidable if there exists a k-avoiding permutation of S.

the recent years have witnessed an increasing attention to the methods of multiple attribute decision making in solving the problems of the real world due to their shorter time of calculation and easy application. one of these methods is the ‘permutation method’ which has a strong logic in connection with ranking issues, but when the number of alternatives increases, solving problems through th...

Kerov polynomials express the normalized characters of irreducible representations of the symmetric group, evaluated on a cycle, as polynomials in the “free cumulants” of the associated Young diagram. We present a positivity conjecture for their coefficients. The latter is stronger than the positivity conjecture due to Kerov and Biane. 1 Kerov polynomials 1.1 Characters A partition λ = (λ1, ......

The set of synchronizing words a given n-state automaton forms regular language recognizable by an with \(2^n - n\) states. size recognizing for the is linked to computational problems related synchronization and length words. Hence, it natural investigate automata extremal this property, i.e., such that minimal deterministic has sync-maximal permutation groups have been introduced in [S. Hoffm...

Let $\mathbb{F}_q$ be the finite field of order $q$, and $\mathbb P^1(\mathbb{F}_q) = \mathbb F_q\cup \{\infty\}$. Write $(x+\sqrt y)^m$ as $N(x,y)+D(x,y)\sqrt{y}$. For $m\in\mathbb N$ $a \in \mathbb{F}_q$, R\'edei function $R_{m,a}\colon P^1(\mathbb F_q) \to F_q)$ is defined by $N(x,a)/D(x,a)$ if $D(x,a)\neq 0$ $x\neq\infty$, $\infty$, otherwise. In this paper we give a complete characterizati...

In the assignment of high-resolution spectra of van der Waals molecular clusters, it is of great utility to know the character table of the molecular symmetry group and the nuclear spin weights of the various rovibronic symmetry species [1]. While their calculation is not difficult, for large groups it is lengthy [2] and prone to errors due to the sheer quantity of variables involved. For the b...