Related papers: On Multisequences and their extensions
In this work we review and derive some elementary properties of the discrete renewal sequences based on a positive, finite and integer-valued random variable. Our results consider these sequences as dependent on the probability masses of…
A class of one-dimensional convolutional codes will be presented. They are all MDS codes, i. e., have the largest distance among all one-dimensional codes of the same length n and overall constraint length delta. Furthermore, their extended…
This paper considers recovering $L$-dimensional vectors $\boldsymbol{w}$, and $\boldsymbol{x}_1,\boldsymbol{x}_2, \ldots, \boldsymbol{x}_N$ from their circular convolutions $\boldsymbol{y}_n = \boldsymbol{w}*\boldsymbol{x}_n, \ n = 1,2,3,…
Let K be a field of characteristic different from 2 and let V be a vector space of dimension n over K. Let M be a non-zero subspace of symmetric bilinear forms defined on V x V and let r=rank(M) denote the set of different positive integers…
A mode of a multiset $S$ is an element $a \in S$ of maximum multiplicity; that is, $a$ occurs at least as frequently as any other element in $S$. Given a list $A[1:n]$ of $n$ items, we consider the problem of constructing a data structure…
This review paper deals with dimension theory of polynomial rings over certain families of pullbacks. While the literature is plentiful, this field is still developing and many contexts are yet to be explored. I will thus restrict the scope…
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…
We give closed form expressions for the numbers of multi-rooted plane trees with specified degrees of root vertices. This results in an infinite number of integer sequences some of which are known to have an alternative interpretation. We…
Frequent sequence mining methods often make use of constraints to control which subsequences should be mined. A variety of such subsequence constraints has been studied in the literature, including length, gap, span, regular-expression, and…
While Large language models (LLMs) have proved able to address some complex reasoning tasks, we also know that they are highly sensitive to input variation, which can lead to different solution paths and final answers. Answer consistency…
Language models are now capable of solving tasks that require dealing with long sequences consisting of hundreds of thousands of tokens. However, they often fail on tasks that require repetitive use of simple rules, even on sequences that…
Let K \subset L be a field extension. Given K-subspaces A,B of L, we study the subspace spanned by the product set AB = {ab | a \in A, b \in B}. We obtain some lower bounds on the dimension of this subspace and on dim B^n in terms of dim A,…
It has been recognized that many complex dynamical systems in the real world require a description in terms of multiplex networks, where a set of common, mutually connected nodes belong to distinct network layers and play a different role…
We give upper-bounds for the dimension of some linear systems. The theorem improves the differential Horace method introduced by Alexander-Hirschowitz, and was conjectured by Simpson. Possible applications are the calculus of the dimension…
Most of the available multivariate statistical models dictate on fitting different parameters for the covariate effects on each multiple responses. This might be unnecessary and inefficient for some cases. In this article, we propose a…
We study the combinatorial function $L(k,q),$ the maximum number of nonzero weights a linear code of dimension $k$ over $\F_q$ can have. We determine it completely for $q=2,$ and for $k=2,$ and provide upper and lower bounds in the general…
The rational covariance extension problem (RCEP) is an important problem in systems and control occurring in such diverse fields as control, estimation, system identification, and signal and image processing, leading to many fundamental…
Given a hyper loop algebra over a non-algebraically closed field, we address multiplicity problems in the underlying abelian tensor category of finite-dimensional representations. Namely, we give formulas for the l-characters of the simple…
We explore a continuum of observably and usefully inequivalent, finite-dimensional off-shell representations of worldline N=4-extended supersymmetry, differing from one another only in the value of a "tuning parameter." Their dynamics turns…
We consider multivariate polynomials and investigate how many zeros of multiplicity at least $r$ they can have over a Cartesian product of finite subsets of a field. Here r is any prescribed positive integer and the definition of…