Related papers: An estimate for the multiplicity of binary recurre…
Working with generating functions, the combinatorics of a recurrence relation can be expressed in a way that allows for more efficient calculation of the quantity. This is true of the Catalan numbers for an ordered binary tree…
This paper studies the problem of recursively estimating the weighted adjacency matrix of a network out of a temporal sequence of binary-valued observations. The observation sequence is generated from nonlinear networked dynamics in which…
By an analogy to the duality between the recurrence time and the longest match length, we introduce a quantity dual to the maximal repetition length, which we call the repetition time. Extending prior results, we sandwich the repetition…
We prove recursive formulas for sums of squares and sums of triangular numbers in terms of sums of divisors functions and we give a variety of consequences of these formulas. Intermediate applications include statements about positivity of…
We present an improved incremental selection algorithm of the selection algorithm presented in [1] and prove all the selected conjectures.
We give a simplified presentation of some results about recurrences of certain sequences of binomial sums in terms of (generalized) Fibonacci and Lucas polynomials.
Let x(n) be a recurrence relation. The main purpose of this article is to determine a recurrence for powers of x(n).
In the paper, the occurrence of zeros and ones in the binary expansion of the primes is studied. In particular the statement in the title is established. The proof is unconditional.
Additive Fourier Transform is sdudied. A fast multiplication algorithm for polynomials over the binary field is given. The bit complexity of the algorithm is $O(n(log n)(\log\log n)^2)$.
We determine the average number of distinct subsequences in a random binary string, and derive an estimate for the average number of distinct subsequences of a particular length.
This paper is devoted to a study of the multiple recurrence of two commuting transformations. We derive a result which is similar but not identical to that of one single transformation established by Bergelson, Host and Kra. We will use the…
This is the central article of a series of three papers on cross product bialgebras. We present a universal theory of bialgebra factorizations (or cross product bialgebras) with cocycles and dual cocycles. We also provide an equivalent…
We provide a recursive construction of all the semi-Heyting algebras that can be defined on a chain with $n$ elements. This construction allows us to count them easily. We also compare the formula for the number of semi-Heyting chains thus…
In this paper the approach to obtaining nonrecurrent formulas for some recursively defined sequences is illustrated. The most interesting result in the paper is the formula for the solution of quadratic map-like recurrence. Also, some…
Within the context of the binomial model, we analyse sequences of values that are almost-uniform and we discuss a prediction method called the frequent outcome approach, in which the outcome that has occurred the most in the observed trials…
We prove that the uniform recurrence of morphic sequences is decidable. For this we show that the number of derived sequences of uniformly recurrent morphic sequences is bounded. As a corollary we obtain that uniformly recurrent morphic…
The regularized product of the Fibonacci numbers is evaluated.
A binary string representation of prime occurrences is a sequence of bits, where $1$ entries encode positions of prime numbers. This is a convenient representation for analysis of prime distribution, since it allows for application of a…
This paper studies algebras arising as algebraic semantics for logics used to model reasoning with incomplete or inconsistent information. In particular we study, in a uniform way, varieties of bilattices equipped with additional…
We derive recursions for the probability distribution of random sums by computer algebra. Unlike the well-known Panjer-type recursions, they are of finite order and thus allow for computation in linear time. This efficiency is bought by the…