Related papers: Combinatorial statistics on restricted growth func…
We consider the question of computing the distribution of a permutation statistics over restricted permutations via enumeration schemes. The restricted permutations are those avoiding sets of vincular patterns (which include both classical…
We introduce the new notion of a conjugate weight function and provide a detailed study of this operation and its properties. Then we apply this knowledge to study classes of ultradifferentiable functions defined in terms of fast growing…
We find a generating function expressed as a continued fraction that enumerates ordered trees by the number of vertices at different levels. Several Catalan problems are mapped to an ordered-tree problem and their generating functions also…
In this paper, we study restricted excludant statistics depending on its parity in partitions where parts with same parity are distinct. Using $q$-series transformations, we show that generating functions of these partition statistics are…
We consider the situation when a learner faces a set of unknown discrete distributions $(p_k)_{k\in \mathcal K}$ defined over a common alphabet $\mathcal X$, and can build for each distribution $p_k$ an individual high-probability…
In the present work, we investigate real numbers whose sequence of partial quotients enjoys some combinatorial properties involving the notion of palindrome. We provide three new transendence criteria, that apply to a broad class of…
We generalize the asymptotic estimates by Bubboloni, Luca and Spiga (2012) on the number of $k$-compositions of $n$ satisfying some coprimality conditions. We substantially refine the error term concerning the number of $k$-compositions of…
We consider uniform random permutations in classes having a finite combinatorial specification for the substitution decomposition. These classes include (but are not limited to) all permutation classes with a finite number of simple…
A descent $k$ of a permutation $\pi=\pi_{1}\pi_{2}\dots\pi_{n}$ is called a big descent if $\pi_{k}>\pi_{k+1}+1$; denote the number of big descents of $\pi$ by $\operatorname{bdes}(\pi)$. We study the distribution of the…
By a classical result of Weyl, for any increasing sequence $(n_k)_{k \geq 1}$ of integers the sequence of fractional parts $(\{n_k x\})_{k \geq 1}$ is uniformly distributed modulo 1 for almost all $x \in [0,1]$. Except for a few special…
In the last decade a huge amount of articles has been published studying pattern avoidance on permutations. From the point of view of enumeration, typically one tries to count permutations avoiding certain patterns according to their…
In this article pattern statistics of typical cubical cut and project sets are studied. We give estimates for the rate of convergence of appearances of patches to their asymptotic frequencies. We also give bounds for repetitivity and…
Partially ordered patterns (POPs) generalize the classical notion of permutation patterns within the framework of pattern avoidance. Building on recent work by Burstein, Han, Kitaev, and Zhang, which introduced the concept of…
In this paper we study restricted overpartitions and concave compositions. In several cases the resulting generating functions involve simultaneously modular forms, mock theta functions, mock Maass theta functions, and false theta…
The arithmetic properties of the ordinary partition function $p(n)$ have been the topic of intensive study for the past century. Ramanujan proved that there are linear congruences of the form $p(\ell n+\beta)\equiv 0\pmod\ell$ for the…
A pattern class is a set of permutations closed under the formation of subpermutations. Such classes can be characterised as those permutations not involving a particular set of forbidden permutations. A simple collection of necessary and…
We determine a lower gap property for the growth of an unbounded \(\mathbb{Z}\)-valued \(k\)-regular sequence. In particular, if \(f:\mathbb{N}\to\mathbb{Z}\) is an unbounded \(k\)-regular sequence, we show that there is a constant \(c>0\)…
The $k$-arrangements are permutations whose fixed points are $k$-colored. We prove enumerative results related to statistics and patterns on $k$-arrangements, confirming several conjectures by Blitvi\'c and Steingr\'imsson. In particular,…
Prior knowledge on properties of a target model often come as discrete or combinatorial descriptions. This work provides a unified computational framework for defining norms that promote such structures. More specifically, we develop…
For each positive integer $k$, we consider five well-studied posets defined on the set of Dyck paths of semilength $k$. We prove that uniquely sorted permutations avoiding various patterns are equinumerous with intervals in these posets.…