Related papers: Order bounds for $C^2$-finite sequences
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…
In this paper, we study the periodicity structure of finite field linear recurring sequences whose period is not necessarily maximal and determine necessary and sufficient conditions for the characteristic polynomial~\(f\) to have exactly…
This paper introduces a class of objects called decision rules that map infinite sequences of alternatives to a decision space. These objects can be used to model situations where a decision maker encounters alternatives in a sequence such…
We characterize vector lattices in which unbounded order convergence is eventually order bounded. Among other things, the characterization provides a solution to \cite[Probl.23]{Az}.
In this paper we give constructions for infinite sequences of finite non-linear locally recoverable codes $\mathcal C\subseteq \prod\limits^N_{i=1}\mathbb F_{q_i}$ over a product of finite fields arising from basis expansions in algebraic…
The aim of this paper is to provide complementary quantitative extensions of two results of H.S. Shapiro on the time-frequency concentration of orthonormal sequences in $L^2 (\R)$. More precisely, Shapiro proved that if the elements of an…
We extend our investigation of $2$-determinants, which we defined in a previous paper. For a linear homogenous recurrence of the second order, we consider relations between different sequences satisfying the same linear homogeneous…
We show that various aspects of k-automatic sequences -- such as having an unbordered factor of length n -- are both decidable and effectively enumerable. As a consequence it follows that many related sequences are either k-automatic or…
This note considers linear recurrences (also called linear difference equations) in unknowns indexed by the integers. We characterize a unique \emph{reduced} linear recurrence with the same solutions as a given linear recurrence, and…
This paper has been withdrawn by the authors due to a crucial computational error. In this paper we deal with the finite case. We prove that a finite bounded ordered set can be represented as the order of principal congruences of a finite…
In a totally ordered set the notion of sorting a finite sequence is defined through a suitable permutation of the sequence's indices. In this paper we prove a simple formula that explicitly describes how the elements of a sequence are…
The classical rearrangement inequality provides bounds for the sum of products of two sequences under permutations of terms and show that similarly ordered sequences provide the largest value whereas opposite ordered sequences provide the…
We consider the functor C that to a unital C*-algebra A assigns the partial order set C(A) of its commutative C*-subalgebras ordered by inclusion. We investigate how some C*-algebraic properties translate under the action of C to…
The notion of lacunary infinite numerical sequence is introduced. It is shown that for an arbitrary linear difference operator L with coefficients belonging to the set R of infinite numerical sequences, a criterion (i.e., a necessary and…
In this paper, we study the product of orders of composition factors of odd order in a composition series of a finite linear group. First we generalize a result by Manz and Wolf about the order of solvable linear groups of odd order. Then…
We characterize the order of principal congruences of a bounded lattice (also of a complete lattice and of a lattice of length 5) as a bounded ordered set. We also state a number of open problems in this new field.
We study log-concavity properties of real sequences $(a_n)_{n \ge 0}$ satisfying a $d$-th order linear recurrence whose coefficients are linear functions of $n$; the so-called P-recursive (or holonomic) sequences. Writing the recurrence in…
We derive an identity connecting any two second-order linear recurrence sequences having the same recurrence relation but whose initial terms may be different. Binomial and ordinary summation identities arising from the identity are…
This paper develops a characterisation of when solutions of forced second order linear differential equations converge to the zero solution of the asymptotically stable and unforced second order equation, or when the solution is bounded,…
Divisibility sequences are defined by the property that their elements divide each other whenever their indices do. The divisibility sequences that also satisfy a linear recurrence, like the Fibonacci numbers, are generated by polynomials…