Related papers: Increasing Consecutive Patterns in Words
Recently, the general problem of enumerating permutations $\pi=\pi_1\cdots \pi_n$ such that $\pi_{i+r}-\pi_i \neq s$ for all $1\leq i\leq n-r$, where $r$ and $s$ are fixed, was considered by Spahn and Zeilberger. In this paper, we consider…
Reliably counting and generating sequences of items remain a significant challenge for neural networks, including Large Language Models (LLMs). Indeed, although this capability is readily handled by rule-based symbolic systems based on…
In [BabStein] Babson and Steingr\'{\i}msson introduced generalized permutation patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. In [Kit1] Kitaev considered simultaneous…
Word2vec (Mikolov et al., 2013) has proven to be successful in natural language processing by capturing the semantic relationships between different words. Built on top of single-word embeddings, paragraph vectors (Le and Mikolov, 2014)…
Learning sentence vectors that generalise well is a challenging task. In this paper we compare three methods of learning phrase embeddings: 1) Using LSTMs, 2) using recursive nets, 3) A variant of the method 2 using the POS information of…
We address the non-redundant random generation of k words of length n from a context-free language. Additionally, we want to avoid a predefined set of words. We study the limits of a rejection-based approach, whose time complexity is shown…
Inversion sequences of length $n$, $\mathbf{I}_n$, are integer sequences $(e_1, \ldots, e_n)$ with $0 \leq e_i < n$ for each $i$. The study of patterns in inversion sequences was initiated recently by Mansour-Shattuck and…
As suggested by Currie, we apply the probabilistic method to problems regarding pattern avoidance. Using techniques from analytic combinatorics, we calculate asymptotic pattern occurrence statistics and use them in conjunction with the…
In this paper we provide an overview of a series of recent results regarding algorithms for searching for subsequences in words or for the analysis of the sets of subsequences occurring in a word.
We introduce operators $\mathsf{hare}$ and $\mathsf{tortoise}$, which act on words as natural generalizations of West's stack-sorting map. We show that the heuristically slower algorithm $\mathsf{tortoise}$ can sort words arbitrarily faster…
Incomplete rankings on a set of items $\{1,\; \ldots,\; n\}$ are orderings of the form $a_{1}\prec\dots\prec a_{k}$, with $\{a_{1},\dots a_{k}\}\subset\{1,\dots,n\}$ and $k < n$. Though they arise in many modern applications, only a few…
This paper discusses an efficient implementation of the generation of order conditions for the construction of exponential integrators like exponential splitting and Magnus-type methods in the computer algebra system Maple. At the core of…
Grammar based compression, where one replaces a long string by a small context-free grammar that generates the string, is a simple and powerful paradigm that captures many popular compression schemes. In this paper, we present a novel…
We present a language independent, unsupervised method for building word embeddings using morphological expansion of text. Our model handles the problem of data sparsity and yields improved word embeddings by relying on training word…
It has been shown that word embeddings derived from large corpora tend to incorporate biases present in their training data. Various methods for mitigating these biases have been proposed, but recent work has demonstrated that these methods…
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 work of thesis we introduce and study a new family of sorting devices, which we call pattern-avoiding machines. They consist of two stacks in series, equipped with a greedy procedure. On both stacks we impose a static constraint in…
Automatic segmentation of text into minimal content-bearing units is an unsolved problem even for languages like English. Spaces between words offer an easy first approximation, but this approximation is not good enough for machine…
Scaling the amount of compute used to train language models has dramatically improved their capabilities. However, when it comes to inference, we often limit models to making only one attempt at a problem. Here, we explore inference compute…
We enumerate permutations that avoid all but one of the $k$ patterns of length $k$ starting with a monotone increasing subsequence of length $k-1$. We compare the size of such permutation classes to the size of the class of permutations…