Related papers: An Analytical Approach to Exponent-Restricted Mult…
The Fermat numbers have many notable properties, including order universality, coprimality, and definition by a recurrence relation. We use arbitrary elliptic curves and rational points of infinite order to generate sequences that are…
Regular sequences are natural generalisations of fixed points of constant-length substitutions on finite alphabets, that is, of automatic sequences. Using the harmonic analysis of measures associated with substitutions as motivation, we…
We associate all small subgraph counting problems with a systematic graph encoding/representation system which makes a coherent use of graphlet structures. The system can serve as a unified foundation for studying and connecting many…
We extend Riemann's rearrangement theorem on conditionally convergent series of real numbers to multiple instead of simple sums.
We study recurrence, and multiple recurrence, properties along the $k$-th powers of a given set of integers. We show that the property of recurrence for some given values of $k$ does not give any constraint on the recurrence for the other…
This dissertation presents a multifaceted look into the structural decomposition of permutation classes. The theory of permutation patterns is a rich and varied field, and is a prime example of how an accessible and intuitive definition…
Sequences that are defined by multisums of hypergeometric terms with compact support occur frequently in enumeration problems of combinatorics, algebraic geometry and perturbative quantum field theory. The standard recipe to study the…
Convergence results for averages of independent replications of counting processes are established in a $p$-variation setting and under certain assumptions. Such convergence results can be combined with functional differentiability results…
In this paper, we study the summability properties of double sequences of real constants which map sequences of random variables to sequences of random variables that are defined on the same probability sample space. We show that a regular…
Until a present, the majority of work in data mining were interested in the extraction of the frequent itemsets and the generation of the frequent association rules from these itemsets. Sometimes, the frequent of associations rules can…
The partial sums of integer sequences that count the occurrences of a specific pattern in the binary expansion of positive integers have been investigated by different authors since the 1950s. In this note, we introduce generalized pattern…
We consider polynomials that are defined as Wronskians of certain sets of Hermite polynomials. Our main result is a recurrence relation for these polynomials in terms of those of one or two degrees smaller, which generalizes the well-known…
Counting distinct permutations with replacement, especially when involving multiple subwords, is a longstanding challenge in combinatorial analysis, with critical applications in cryptography, bioinformatics, and statistical modeling. This…
Given a random text over a finite alphabet, we study the frequencies at which fixed-length words occur as subsequences. As the data size grows, the joint distribution of word counts exhibits a rich asymptotic structure. We investigate all…
The aim of this note is to show the existence of a correspondance between certain algebraic continued fractions in fields of power series over a finite field and automatic sequences in the same finite field. this connection is illustrated…
The document tries to put focus on sequences with certain properties and periods leading to the first value smaller than the starting value in the Collatz problem. With the idea that, if all starting numbers lead ultimately to a smaller…
Recent studies on frequent itemset mining algorithms resulted in significant performance improvements. However, if the minimal support threshold is set too low, or the data is highly correlated, the number of frequent itemsets itself can be…
In this paper, we clarified the relationship between continued fractions, determinants, and identities, making it easier to apply these methods systematically in other settings. In particular, we studied finite continued fractions from the…
By using the matrix formulation of the two-step approach to the distributions of runs, a recursive relation and an explicit expression are derived for the generating function of the joint distribution of rises and falls for multivariate…
Regular variation is a continuous-parameter theory; we work in a general setting, containing the existing Karamata, Bojanic-Karamata/de Haan and Beurling theories as special cases. We give sequential versions of the main theorems, that is,…