Related papers: The cycle descent statistic on permutations
We prove the universality of the large deviations for conjugacy invariant permutations with few cycles. As an application, we establish the universality of large deviation at speeds $n$ and $\sqrt{n}$ for the length of monotone subsequences…
We obtain large and moderate deviation estimates, as well as concentration inequalities, for a class of nonuniformly expanding maps with stretched exponential decay of correlations. In the large deviation regime, we also exhibit examples…
Convolution sums are introduced and special instances of the cyclic convolution on finite sets is examined in more detail. The distributions that emerge are multidimensional generalizations of the Catalan and Narayana numbers. This work…
We use moment method to understand the cycle structure of the composition of independent invariant permutations. We prove that under a good control on fixed points and cycles of length 2, the limiting joint distribution of the number of…
We introduce the cycle intersection graph of a graph, an adaptation of the cycle graph of a graph, and use the structure of these graphs to prove an upper bound for the decycling number of all even graphs. This bound is shown to be…
We complete the enumeration of Dumont permutations of the second kind avoiding a pattern of length 4 which is itself a Dumont permutation of the second kind. We also consider some combinatorial statistics on Dumont permutations avoiding…
In this paper, several variants of the ascent-plateau statistic are introduced, including flag ascent-plateau, double ascent and descent-plateau. We first study the flag ascent-plateau statistic on Stirling permutations by using…
We investigate a descent on simple graphs, starting with the complete graph on $n$ vertices and ending up with the cycle graph by removing one edge after another. We obtain quantitative results showing that graphs with large diameter must…
We compute the limiting distribution, as n approaches infinity, of the number of cycles of length between gamma n and delta n in a permutation of [n] chosen uniformly at random, for constants gamma, delta such that 1/(k+1) <= gamma < delta…
A sequence of reversals that takes a signed permutation to the identity is perfect if at no step a common interval is broken. Determining a parsimonious perfect sequence of reversals that sorts a signed permutation is NP-hard. Here we show…
We establish upper and lower bounds on the maximal number of steps needed to transform a cyclic permutation to the canonical cyclic permutation using conjugation by adjacent transpositions, and on the diameter of the underlying Schreier…
We discuss and prove a number of results for calculating characteristic cycles, or graded, enriched characteristic cycles. We concentrate particularly on results related to hypersurfaces.
We consider the cycle structure of a random permutation $\sigma$ chosen uniformly from the symmetric group, subject to the constraint that $\sigma$ does not contain cycles of length exceeding $r.$ We prove that under suitable conditions the…
In this short note, we classify the degree-inverting involution on the full square and triangular matrices.
A cyclic random walk is a random walk whose transition probabilities/rates can be written as a superposition of the empirical measures of a family of finite cycles. This identifies a convex set of models. We discuss the problem of…
We introduce a new approach to an enumerative problem closely linked with the geometry of branched coverings; that is, we study the number of ways a permutation can be decomposed into a product of a given number of 2-cycles, 3-cycles, etc.…
We investigate fixed points and cycle types of permutation polynomials and complete permutation polynomials arising from reversed Dickson polynomials of the first kind and second kind over $\mathbb{F}_p$. We also study the permutation…
In this paper we introduce {\em weak ascent sequences}, a class of number sequences that properly contains ascent sequences. We show how these sequences uniquely encode each of the following objects: permutations avoiding a particular…
We study the continuous-time evolution of the recombination equation of population genetics. This evolution is given by a differential equation that acts on a product probability space, and its solution can be described by a Markov chain on…
In this paper, we count a dual set of Stirling permutations by the number of alternating runs. Properties of the generating functions, including recurrence relations, grammatical interpretations and convolution formulas are studied.