In this paper, we study tree–like tableaux, combinatorial objects which exhibit a natural tree structure and are connected to the partially asymmetric simple exclusion process (PASEP). There was a conjecture made on the total number of corners in tree–like tableaux and the total number of corners in symmetric tree–like tableaux. In this paper, we prove both conjectures. Our proofs are based on ...

A minimal permutation representation of a finite group G is a faithful G-set with the smallest possible cardinality. We study the structure of such representations and show that for most groups they may be obtained by a greedy construction. It follows that whenever the algorithm works (except when central involutions intervene) all minimal permutation representations have the same set of orbit ...

In order to develop fast and robust methods for extracting qualitative information from non-linear time series, Bandt and Pompe have proposed to consider time series from the pure ordinal viewpoint. On the base of counting ordinal patterns, which describe the up-and-down in a time series, they have introduced the concept of permutation entropy for quantifying the complexity of a system behind a...

A minimal permutation representation of a finite group G is a faithful G-set with the smallest possible size. We study the structure of such representations and show that for certain groups they may be obtained by a greedy construction. In these situations (except when central involutions intervene) all minimal permutation representations have the same set of orbit sizes. Using the same ideas w...

introduction: in this paper, a novel complexity measure is proposed to detect dynamical changes in nonlinear systems using ordinal pattern analysis of time series data taken from the system. epilepsy is considered as a dynamical change in nonlinear and complex brain system. the ability of the proposed measure for characterizing the normal and epileptic eeg signals when the signal is short or is...

Let C be a conjugation class of permutations of a finite field Fq. We consider the function NCðqÞ defined as the number of permutations in C for which the associated permutation polynomial has degree 5q 2. In 1969, Wells proved a formula for N1⁄23 ðqÞ where 1⁄2k denotes the conjugation class of k-cycles. We will prove formulas for N1⁄2k ðqÞ where k 1⁄4 4; 5; 6 and for the classes of permutation...

We show that the problem of counting collinear points in a permutation (previously considered by the author and J. Solymosi in [1]) and the well-known finite plane Kakeya problem are intimately connected. Via counting arguments and by studying the hypergraph of collinear triples we show a new lower bound (25q/72 + O(1)) for the number of collinear triples of a permutation of Fq and a new lower ...

We describe a family of new algorithms for finding the canonical image of a set of points under the action of a permutation group. This family of algorithms makes use of the orbit structure of the group, and a chain of subgroups of the group, to efficiently reduce the amount of search which must be performed to find a canonical image. We present both a formal proof of correctness of our algorit...

We discuss Lachlan’s classification theory for finite homogeneous structures and related problems on finite permutation groups. Lachlan’s theory provides a hierarchy of classifications in which structures which are “sporadic” in one context reappear as members of infinite families at later stages. Every finite structure is accounted for at some level in this hierarchy, but for structures associ...

Modeling proximity searching problems in a metric space allows one to approach many problems in different areas, e.g. pattern recognition, multimedia search, or clustering. Recently there was proposed the permutation based approach, a novel technique that is unbeatable in practice but difficult to compress. In this article we introduce an improvement on that metric space search data structure. ...