Related papers: Counting occurrences of some subword patterns
Following Inoue et al., we define a word to be a repetition if it is a (fractional) power of exponent at least 2. A word has a repetition factorization if it is the product of repetitions. We study repetition factorizations in several…
We use a probabilistic method to produce some combinatorial inequalities by considering pattern containment in permutations and words.
Data mining is the task of discovering interesting patterns from large amounts of data. There are many data mining tasks, such as classification, clustering, association rule mining, and sequential pattern mining. Sequential pattern mining…
Building meaningful representations of noun compounds is not trivial since many of them scarcely appear in the corpus. To that end, composition functions approximate the distributional representation of a noun compound by combining its…
We prove that generating subspaces of matrix rings over finite fields are counted by polynomials. We use this result to define and study two-variable versions of polynomials counting isomorphism classes of absolutely irreducible…
We define impulse response sequence in the set of all linear recurring sequences satisfying a linear recurrence relation of order $r$. The generating function and expression of the impulse response sequence are presented. Some identities of…
Consider a subfield of the field of rational functions in several indeterminates. We present an algorithm that, given a set of generators of such a subfield, finds a simple generating set. We provide an implementation of the algorithm and…
This paper provides a geometric characterization of subclasses of the regular languages. We use finite model theory to characterize objects like strings and trees as relational structures. Logical statements meeting certain criteria over…
Current approaches in paraphrase generation and detection heavily rely on a single general similarity score, ignoring the intricate linguistic properties of language. This paper introduces two new tasks to address this shortcoming by…
In this paper, we study the generating functions for the number of pattern restricted Stirling permutations with a given number of plateaus, descents and ascents. Properties of the generating functions, including symmetric properties and…
We consider a programming language based on the lamplighter group that uses only composition and iteration as control structures. We derive generating functions and counting formulas for this language and special subsets of it, establishing…
Closed-form generating functions for counting one-face rooted hypermaps with a known number of darts by number of vertices and edges is found, using matrix integral expressions relating to the reduced density operator of a bipartite quantum…
We use the generating function of the characters of $C_2$ to obtain a generating function for the multiplicities of the weights entering in the irreducible representations of that simple Lie algebra. From this generating function we derive…
Let P be a poset and let P* be the set of all finite length words over P. Generalized subword order is the partial order on P* obtained by letting u \leq w if and only if there is a subword u' of w having the same length as u such that each…
A classical result by Guibas and Odlyzko obtained in 1981 gives the generating function for the number of strings that avoid a given set of substrings with the property that no substring is contained in any of the others. In this paper, we…
A computational model of the construction of word meaning through exposure to texts is built in order to simulate the effects of co-occurrence values on word semantic similarities, paragraph by paragraph. Semantic similarity is here viewed…
In this article we generalize packing density problems from permutations to patterns with repeated letters and generalized patterns. We are able to find the packing density for some classes of patterns and several other short patterns.
We regard explanations as a blending of the input sample and the model's output and offer a few definitions that capture various desired properties of the function that generates these explanations. We study the links between these…
In this work we define a unified generating functions for 9 different kinds of set partitions including cyclically ordered set partitions. Such generating function depends on 4 parameters. We consider property of this function and provide…
We study here the so called subsequence pattern matching also known as hidden pattern matching in which one searches for a given pattern $w$ of length $m$ as a subsequence in a random text of length $n$. The quantity of interest is the…