Related papers: Classical length-5 pattern-avoiding permutations
Some authors have recently argued that a finite-size scaling law for the text-length dependence of word-frequency distributions cannot be conceptually valid. Here we give solid quantitative evidence for the validity of such scaling law,…
For a set of permutation patterns $\Pi$, let $F^\text{st}_n(\Pi,q)$ be the st-polynomial of permutations avoiding all patterns in $\Pi$. Suppose $312\in\Pi$. For a class of permutation statistics which includes inversion and descent…
Percolation on a five-dimensional simple hypercubic (sc(5)) lattice with extended neighborhoods is investigated by means of extensive Monte Carlo simulations, using an effective single-cluster growth algorithm. The critical exponents,…
Finding distributions of statistics in pattern-avoiding permutations has attracted significant attention in the literature. In particular, Chen, Kitaev, and Zhang derived functional equations for the joint distributions of any subset of…
We study the distribution of the statistics 'number of fixed points' and 'number of excedances' in permutations avoiding subsets of patterns of length 3. We solve all the cases of simultaneous avoidance of more than one pattern, giving…
One of the most challenging problems in enumerative combinatorics is to count Wilf classes, where you are given a pattern, or set of patterns, and you are asked to find a "formula", or at least an efficient algorithm, that inputs a positive…
Can one hear the 'sound' of a growing network? We address the problem of recognizing the topology of evolving biological or social networks. Starting from percolation theory, we analytically prove a linear inverse relationship between two…
Inversion sequences are finite sequences of non-negative integers, where the value of each entry is bounded from above by its position. Patterns in inversion sequences have been studied by Corteel-Martinez-Savage-Weselcouch and…
In this paper, we enumerate two families of pattern-avoiding permutations: those avoiding the vincular pattern $2-41-3$, which we call semi-Baxter permutations, and those avoiding the vincular patterns $2-41-3$, $3-14-2$ and $3-41-2$, which…
This paper aims to contribute to validate, for numerical semigroups of reasonably large genus, the so-called Conjecture of Wilf. There is no counter-example for the conjecture among the over 3*10^{10} numerical semigroups of genus up to 60,…
The growth dynamics of complex systems often exhibit statistical regularities involving power-law relationships. For real finite complex systems formed by countable tokens (animals, words) as instances of distinct types (species, dictionary…
We present a class of permutations for which the number of distinctly ordered subsequences of each permutation approaches an almost optimal value as the length of the permutation grows to infinity.
We consider a random permutation drawn from the set of 132-avoiding permutations of length $n$ and show that the number of occurrences of another pattern $\sigma$ has a limit distribution, after scaling by $n^{\lambda(\sigma)/2}$ where…
In this paper we consider the enumeration of ordered set partitions avoiding a permutation pattern of length 2 or 3. We provide an exact enumeration for avoiding the permutation 12. We also give exact enumeration for ordered partitions with…
We consider a special class of weak dependent random variables with control on covariances of Lipschitz transformations. This class includes, but is not limited to, positively, negatively associated variables and a few other classes of…
With the number of sequenced genomes now over one hundred, and the availability of rough functional annotations for a substantial proportion of their genes, it has become possible to study the statistics of gene content across genomes. Here…
We introduce a non-growth model that generates the power-law distribution with the Zipf exponent. There are N elements, each of which is characterized by a quantity, and at each time step these quantities are redistributed through binary…
We provide a large class of functions $f$ that are bell-shaped: the $n$-th derivative of $f$ changes its sign exactly $n$ times. This class is described by means of Stieltjes-type representation of the logarithm of the Fourier transform of…
In this dissertation we examine the relationships between the several hierarchies, including the complexity, $\mathrm{LUA}$ (Linearly Universal Avoidance), and shift complexity hierarchies, with an eye towards quantitative bounds on growth…
We initiate a systematic study of pattern avoidance in rectangulations. We give a formal definition of such patterns and investigate rectangulations that avoid $\top$-like patterns - the pattern $\top$ and its rotations. For every $L…