相关论文: Packing patterns into words
We provide upper and lower bounds for the expected length $\mathbb E(L_{n,m})$ of the longest common pattern contained in $m$ random permutations of length $n$. We also address the tightness of the concentration of $L_{n,m}$ around $\mathbb…
Given a countable set X (usually taken to be the natural numbers or integers), an infinite permutation, \pi, of X is a linear ordering of X. This paper investigates the combinatorial complexity of infinite permutations on the natural…
We approach the problem of generalizing pre-trained word embeddings beyond fixed-size vocabularies without using additional contextual information. We propose a subword-level word vector generation model that views words as bags of…
We find exact formulas and/or generating functions for the number of words avoiding 3-letter generalized multipermutation patterns and find which of them are equally avoided.
We study compressible types in the context of (local and global) NIP. By extending a result in machine learning theory (the existence of a bound on the recursive teaching dimension), we prove density of compressible types. Using this, we…
We generally study the density of eigenvalues in unitary ensembles of random matrices from the recurrence coefficients with regularly varying conditions for the orthogonal polynomials. First we calculate directly the moments of the density.…
Discovering patterns from data is an important task in data mining. There exist techniques to find large collections of many kinds of patterns from data very efficiently. A collection of patterns can be regarded as a summary of the data. A…
Models of bags of words typically assume topic mixing so that the words in a single bag come from a limited number of topics. We show here that many sets of bag of words exhibit a very different pattern of variation than the patterns that…
We study scaling limits of random permutations ("permutons") constrained by having fixed densities of a finite number of patterns. We show that the limit shapes are determined by maximizing entropy over permutons with those constraints. In…
We find generating functions the number of strings (words) containing a specified number of occurrences of certain types of order-isomorphic classes of substrings called subword patterns. In particular, we find generating functions for the…
We study the cycle structure of words in several random permutations. We assume that the permutations are independent and that their distribution is conjugation invariant, with a good control on their short cycles. If, after successive…
There is a deep connection between permutations and trees. Certain sub-structures of permutations, called sub-permutations, bijectively map to sub-trees of binary increasing trees. This opens a powerful tool set to study enumerative and…
Recent observations in the theory of verse and empirical metrics have suggested that constructing a verse line involves a pattern-matching search through a source text, and that the number of found elements (complete words totaling a…
In this survey we give an overview about some of the main results on parametric densities, a concept which unifies the theory of finite (free) packings and the classical theory of infinite packings.
An infinite permutation is a linear ordering of the set of non-negative integers. Generally, the properties of infinite permutations analogous to those of infinite words show some resemblances and some differences between permutations and…
Current work in lexical distributed representations maps each word to a point vector in low-dimensional space. Mapping instead to a density provides many interesting advantages, including better capturing uncertainty about a representation…
We offer elementary proofs for several results in consecutive pattern containment that were previously demonstrated using ideas from cluster method and analytical combinatorics. Furthermore, we establish new general bounds on the growth…
We study density of rational languages under shift invariant probability measures on spaces of two-sided infinite words, which generalizes the classical notion of density studied in formal languages and automata theory. The density for a…
The method we have applied in "A. Bernini, L. Ferrari, R. Pinzani, Enumerating permutations avoiding three Babson-Steingrimsson patterns, Ann. Comb. 9 (2005), 137--162" to count pattern avoiding permutations is adapted to words. As an…
We study the relation between the palindromic and factor complexity of infinite words. We show that for uniformly recurrent words one has P(n)+P(n+1) \leq \Delta C(n) + 2, for all n \in N. For a large class of words it is a better estimate…