Related papers: A New Operation on Sequences: the Boustrouphedon T…
The "Choix de Bruxelles" operation replaces a positive integer n by any of the numbers that can be obtained by halving or doubling a substring of the decimal representation of n. For example, 16 can become any of 16, 26, 13, 112, 8, or 32.…
We consider the transform from sequences to triangular arrays defined in terms of generating functions by f(x) -> (1-x)/(1-xy) f(x(1-x)/(1-xy)). We establish a criterion for the transform of a nonnegative sequence to be nonnegative, and we…
We discuss interplays between log-concave functions and log-concave sequences. We prove a Bernstein-type theorem, which characterizes the Laplace transform of log-concave measures on the half-line in terms of log-concavity of the…
The paper presents a new generalized integer orthogonal transformation which consists of a well known orthogonal transform followed by stretching the basis vectors maintaining the asymptotic behavior of the number of integer solutions for…
Current neural architectures lack a principled way to handle interchangeable tokens, i.e., symbols that are semantically equivalent yet distinguishable, such as bound variables. As a result, models trained on fixed vocabularies often…
In this paper we investigate a permutation statistic that was independently introduced by Romik in 2005. This statistic counts the number of bumps that occur during the execution of the Robinson-Schensted procedure when applied to a given…
The boson-fermion correspondences are an important phenomena on the intersection of several areas in mathematical physics: representation theory, vertex algebras and conformal field theory, integrable systems, number theory, cohomology. Two…
We consider the $osp(1|2)$-invariant bilinear operations on weighted densities on the supercircle $S^{1|1}$ called the supertransvectants. These operations are analogues of the famous Gordan transvectants (or Rankin-Cohen brackets). 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…
Modern neural sequence generation models are built to either generate tokens step-by-step from scratch or (iteratively) modify a sequence of tokens bounded by a fixed length. In this work, we develop Levenshtein Transformer, a new partially…
We study a new kind of Courant algebroid on Poisson manifolds, which is a variant of the generalized tangent bundle in the sense that the roles of tangent and the cotangent bundle are exchanged. Its symmetry is a semidirect product of…
The paperfolding sequences form an uncountable class of infinite sequences over the alphabet $\{ -1, 1 \}$ that describe the sequence of folds arising from iterated folding of a piece of paper, followed by unfolding. In this note we observe…
In this paper we use techniques in Fock spaces theory and compute how the Segal-Bargmann transform acts on special wave functions obtained by multiplying superoscillating sequences with normalized Hermite functions. It turns out that these…
Multifractal scaling has been extensively studied for real-valued stochastic processes, but a systematic integer-valued analogue has remained largely unexplored. In this work, we introduce a multifractal framework for integer-valued…
A superpermutation is a sequence that contains every permutation of $n$ distinct symbols as a contiguous substring. For instance, a valid example for three symbols is a sequence that contains all six permutations. This paper introduces a…
We find the exponential generating function for permutations with all valleys even and all peaks odd, and use it to determine the asymptotics for its coefficients, answering a question posed by Liviu Nicolaescu. The generating function can…
This paper presents a novel variant of the Broyden quasi-Newton secant-type method aimed at solving constrained mixed generalized equations, which can include functions that are not necessarily differentiable. The proposed method integrates…
In this report, we introduce PE-AONT: a novel algorithm for fast and secure data fragmentation. Initial data are fragmented and only a selected subset of the fragments is encrypted. Further, fragments are transformed using a variation of an…
The realization of robust universal quantum computation with any platform ultimately requires both the coherent storage of quantum information and (at least) one entangling operation between individual elements. The use of…
Operators on probability distributions can be expressed as operators on the associated moment sequences, and so correspond to operators on integer sequences. Thus, there is an opportunity to apply each theory to the other. Moreover,…