Related papers: Permutation patterns: basic definitions and notati…
In this dissertation, we explore the structure of inversion graphs of permutations--a class of graphs that naturally arises by representing each permutation as a graph, where vertices correspond to entries and edges encode inversions.…
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 count the number of occurrences of restricted patterns of length 3 in permutations with respect to length and the number of cycles. The main tool is a bijection between permutations in standard cycle form and weighted Motzkin paths.
In this paper we begin the first systematic study of distributions of simple marked mesh patterns. Mesh patterns were introduced recently by Br\"and\'en and Claesson in connection with permutation statistics. We provide explicit generating…
We present an overview of selected topics in random permutations and random partitions highlighting analogies with random matrix theory.
Permutation polynomials over finite fields play important roles in finite fields theory. They also have wide applications in many areas of science and engineering such as coding theory, cryptography, combinatorial design, communication…
We review how the monotone pattern compares to other patterns in terms of enumerative results on pattern avoiding permutations. We consider three natural definitions of pattern avoidance, give an overview of classic and recent formulas, and…
We study relationships between permutation statistics and pattern-functions, counting the number of times particular patterns occur in a permutation. This allows us to write several familiar statistics as linear combinations of pattern…
The classes of tree permutations and forest permutations were defined by Acan and Hitczenko (2016). We study random permutations of a given length from these classes, and in particular the number of occurrences of a fixed pattern in one of…
Modellers of large scale genome rearrangement events, in which segments of DNA are inverted, moved, swapped, or even inserted or deleted, have found a natural syntax in the language of permutations. Despite this, there has been a wide range…
This is a concise overview of the definitions and properties of the linking number and its higher-order generalization, Milnor invariants.
The use of patterns in predictive models is a topic that has received a lot of attention in recent years. Pattern mining can help to obtain models for structured domains, such as graphs and sequences, and has been proposed as a means to…
Motivated by the problem of constructing bijective maps with low differential uniformity, we introduce the notion of permutation resemblance of a function, which looks to measure the distance a given map is from being a permutation. We…
In this article we generalize packing density problems from permutations to patterns with repeated letters and generalized patterns. We are able to find the packing density for some classes of patterns and several other short patterns.
Models of period variations are basic tools for period analyzes of variable stars. We introduce phase function and instant period and formulate basic relations and equations among them. Some simple period models are also presented.
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…
We define a statistic on the graph of commutation classes of a permutation of the symmetric group which is used to show that these graphs are equipped with a ranked poset structure, with a minimum and maximum. This characterization also…
A deflatable permutation class is one in which the simple permutations are contained in a proper subclass. Deflatable permutation classes are often easier to describe and enumerate than non-deflatable ones. Some theorems which guarantee…
We review and extend previous results on coincidence of mesh patterns. We introduce the notion of a force on a permutation pattern and apply it to the coincidence classification of mesh patterns, completing the classification up to size…
This article introduces patterns of ideals of numerical semigroups, thereby unifying previous definitions of patterns of numerical semigroups. Several results of general interest are proved. More precisely, this article presents results on…