Related papers: On a Central Transform of Integer Sequences
Linear processes are defined as a discrete-time convolution between a kernel and an infinite sequence of i.i.d. random variables. We modify this convolution by introducing decimation, that is, by stretching time accordingly. We then…
We introduce a method for calculating individual elements of matrix functions. Our technique makes use of a novel series expansion for the action of matrix functions on basis vectors that is memory efficient even for very large matrices. We…
In this paper, we give recurrence relations and identities for some integer sequences related to Ward numbers such as Ward-Lah numbers, varied Ward numbers and binomial Ward numbers. Most of the sequences are entered in the On-Line…
An integer sequence that is defined by initial values and a linear recurrence with constant integer coefficients, can be represented by the difference of two arithmetic terms containing exponentiation. All constants occuring in the term are…
Self-attentive transformer models have recently been shown to solve the next item recommendation task very efficiently. The learned attention weights capture sequential dynamics in user behavior and generalize well. Motivated by the special…
Bijections between invariants associated to indecomposable projective modules over some suitable Brauer configuration algebras and invariants associated to solutions of the Kronecker problem and the four subspace problem are used to…
In this paper we study the action of the Binomial and Invert (interpolated) operators on the set of linear recurrent sequences. We prove that these operators preserve this set, and we determine how they change the characteristic…
What is Sequence Algebra? This is a question that any teacher or student of mathematics or computer science can engage with. Sequences are in Calculus, Combinatorics, Statistics and Computation. They are foundational, a step up from number…
A minimal homogeneous generating system of the algebra of semi-invariants of tuples of two-by-two matrices over an infinite field of characteristic two or over the ring of integers is given. In an alternative interpretation this yields a…
We translate the concept of succession rule and the ECO method into matrix notation, introducing the concept of a production matrix. This allows us to combine our method with other enumeration techniques using matrices, such as the method…
We use elementary triangular matrices to obtain some factorization, multiplication, and inversion properties of triangular matrices. We also obtain explicit expressions for the inverses of strict $k$-Hessenberg matrices and banded matrices.…
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…
We present a general theory of fractal transformations and show how it leads to a new type of method for filtering and transforming digital images. This work substantially generalizes earlier work on fractal tops. The approach involves…
We deal with a class of one-parameter family of integral transforms of Bargmann type arising as dual transforms of fractional Hankel transform. Their ranges are identified to be special subspaces of the weighted hyperholomorphic left…
We examine a class of embeddings based on structured random matrices with orthogonal rows which can be applied in many machine learning applications including dimensionality reduction and kernel approximation. For both the…
This paper is the continuation of \cite{htl}, where we deal with Lucas sequences. Here we study integers represented by integer sequences which satisfy binary recursive relations. In case of non-degenerate sequences we give bounds for the…
Convergence problems occur abundantly in all branches of mathematics or in the mathematical treatment of the sciences. Sequence transformations are principal tools to overcome convergence problems of the kind. They accomplish this by…
Most existing Neural Machine Translation models use groups of characters or whole words as their unit of input and output. We propose a model with a hierarchical char2word encoder, that takes individual characters both as input and output.…
A pattern of a sequence is a sequence of integer indices with each index describing the order of first occurrence of the respective symbol in the original sequence. In a recent paper, tight general bounds on the block entropy of patterns of…
A brief overview of some computer algebra methods for computations with nested integrals is given. The focus is on nested integrals over integrands involving square roots. Rewrite rules for conversion to and from associated nested sums are…