Related papers: The peak statistics on simsun permutations

Random permutation set (RPS), as a recently proposed theory, enables powerful information representation by traversing all possible permutations. However, the repetition of items is not allowed in RPS while it is quite common in real life.…

In this paper, we extend the notion of labeled partitions with ordinary permutations to colored permutations in the sense that the colors are endowed with a cyclic structure. We use labeled partitions with colored permutations to derive the…

The main goal of this paper is to study the different definitions of generating sequences appearing in the literature. We present these definitions and show that under certain situations they are equivalent. We also present an example that…

In his Ph.D. thesis, Ira Gessel proved a reciprocity formula for noncommutative symmetric functions which enables one to count words and permutations with restrictions on the lengths of their increasing runs. We generalize Gessel's theorem…

A permutation is centrosymmetric if it is fixed by a half-turn rotation of its diagram. Initially motivated by a question by Alexander Woo, we investigate the question of whether the growth rate of a permutation class equals the growth rate…

We describe birational representations of discrete groups generated by involutions, having their origin in the theory of exactly solvable vertex-models in lattice statistical mechanics. These involutions correspond respectively to two kinds…

Let $G_{k,n}$ be a group of permutations of $kn$ objects which permutes things independently in disjoint blocks of size $k$ and then permutes the blocks. We investigate the probabilistic and/or enumerative aspects of random elements of…

The number of peaks of a random permutation is known to be asymptotically normal. We give a new proof of this and prove a central limit theorem for the distribution of peaks in a fixed conjugacy class of the symmetric group. Our technique…

It is observed that the conjugacy growth series of the infinite fini-tary symmetric group with respect to the generating set of transpositions is the generating series of the partition function. Other conjugacy growth series are computed,…

Let $(P_n)_n$ and $(Q_n)_n$ be two sequences of monic polynomials linked by a type structure relation such as $$ Q_{n}(x)+r_nQ_{n-1}(x)=P_{n}(x)+s_nP_{n-1}(x)+t_nP_{n-2}(x)\;, $$ where $(r_n)_n$, $(s_n)_n$ and $(t_n)_n$ are sequences of…

We focus on writing closed forms of generating functions for the number of partitions with gap conditions as double sums starting from a combinatorial construction. Some examples of the sets of partitions with gap conditions to be discussed…

We present an overview of selected topics in random permutations and random partitions highlighting analogies with random matrix theory.

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…

Working with generating functions, the combinatorics of a recurrence relation can be expressed in a way that allows for more efficient calculation of the quantity. This is true of the Catalan numbers for an ordered binary tree…

By a classical principle of analysis, sufficiently thin subsequences of general sequences of functions behave like sequences of independent random variables. This observation not only explains the remarkable properties of lacunary…

For any finite poset we define a generating polynomial counting upsets, downsets, and their intersection. We investigate the behaviour of this polynomial with respect to poset operations, show that it distinguishes series-parallel posets,…

It has been recently discovered that some random processes may satisfy limit theorems even though they exhibit intermittency, namely an unusual growth of moments. In this paper we provide a deeper understanding of these intricate limiting…

Statistics in ranked lists is important in analyzing molecular biology measurement data, such as ChIP-seq, which yields ranked lists of genomic sequences. State of the art methods study fixed motifs in ranked lists. More flexible models…

Let $n \ge 3$ be an integer. Let $P_n = \{1, 2, 3, ..., n-1, n \}$ and let $S_n$ be the symmetric group of permutations on $P_n$. Motivated by the theory of discrete dynamical systems on the interval, we associate each permutation $\si_n$…

Recently it has been shown that all non-trivial closed permutation groups containing the automorphism group of the random poset are generated by two types of permutations: the first type are permutations turning the order upside down, and…