Related papers: Counting Small Permutation Patterns
The problem of genealogy of permutations has been solved partially by Stefan (odd order) and Acosta-Hum\'anez & Bernhardt (power of two). It is well known that Sharkovskii's theorem shows the relationship between the cardinal of the set of…
In this work we introduce and study tree-like tableaux, which are certain fillings of Ferrers diagrams in simple bijection with permutation tableaux and alternative tableaux. We exhibit an elementary insertion procedure on our tableaux…
The idea of counting the number of satisfying truth assignments (models) of a formula by adding random parity constraints can be traced back to the seminal work of Valiant and Vazirani, showing that NP is as easy as detecting unique…
We consider uniform random permutations drawn from a family enumerated through generating trees. We develop a new general technique to establish a central limit theorem for the number of consecutive occurrences of a fixed pattern in such…
Cartesian tree matching is the problem of finding all substrings of a given text which have the same Cartesian trees as that of a given pattern. So far there is one linear-time solution for Cartesian tree matching, which is based on the KMP…
A cornerstone of human statistical learning is the ability to extract temporal regularities / patterns from random sequences. Here we present a method of computing pattern time statistics with generating functions for first-order Markov…
We present the first sub-quadratic time algorithm that with high probability correctly reconstructs phylogenetic trees for short sequences generated by a Markov model of evolution. Due to rapid expansion in sequence databases, such very…
This paper gives a new algorithm for sampling tree-weighted partitions of a large class of planar graphs. Formally, the tree-weighted distribution on $k$-partitions of a graph weights $k$-partitions proportional to the product of the number…
In this paper, we present a deterministic variant of Chan's randomized partition tree [Discret. Comput. Geom., 2012]. This result leads to numerous applications. In particular, for $d$-dimensional simplex range counting (for any constant $d…
The two main approaches to the study of irreducible representations of orders (via traces and Poisson orders) have so far been applied in a completely independent fashion. We define and study a natural compatibility relation between the two…
Ordinal Patterns are a time-series data analysis tool used as a preliminary step to construct the Permutation Entropy which itself allows the same characterization of dynamics as chaotic or regular as more theoretical constructs such as the…
Frequent pattern mining is a flagship problem in data mining. In its most basic form, it asks for the set of substrings of a given string $S$ of length $n$ that occur at least $\tau$ times in $S$, for some integer $\tau\in[1,n]$. We…
Odlyzko has computed a data set listing more than $10^9$ successive Riemann zeros, starting at a zero number beyond $10^{23}$. The data set relates to random matrix theory since, according to the Montgomery-Odlyzko law, the statistical…
We consider a random permutation drawn from the set of permutations of length $n$ that avoid some given set of patterns of length 3. We show that the number of occurrences of another pattern $\sigma$ has a limit distribution, after suitable…
Given a pattern $P$ and a text $T$, both strings over a binary alphabet, the binary jumbled string matching problem consists in telling whether any permutation of $P$ occurs in $T$. The indexed version of this problem, i.e., preprocessing a…
We study the computational complexity of approximately computing the partition function of a spin system. Techniques based on standard counting-to-sampling reductions yield $\tilde{O}(n^2)$-time algorithms, where $n$ is the size of the…
Let $w$ be a string of length $n$. The problem of counting factors crossing a position - Problem 64 from the textbook ``125 Problems in Text Algorithms'' [Crochemore, Leqroc, and Rytter, 2021], asks to count the number $\mathcal{C}(w,k)$…
The problem of genealogy of permutations has been solved partially by Stefan (odd order) and Acosta-Hum\'anez \& Bernhardt (power of two). It is well known that Sharkovskii's theorem shows the relationship between the cardinal of the set of…
Quantum computations are typically compiled into a circuit of basic quantum gates. Just like for classical circuits, a quantum compiler should optimize the quantum circuit, e.g. by minimizing the number of required gates. Optimizing quantum…
The order $O_n(\sigma)$ of a permutation $\sigma$ of $n$ objects is the smallest integer $k \geq 1$ such that the $k$-th iterate of $\sigma$ gives the identity. A remarkable result about the order of a uniformly chosen permutation is due to…