Related papers: Strongly k-recursive sequences

Given a simple undirected graph, one can construct from it a $c$-step nilpotent Lie algebra for every $c \geq 2$ and over any field $K$, in particular also over the real and complex numbers. These Lie algebras form an important class of…

Polynomially-recursive sequences generally have a periodic behavior mod $m$. In this paper, we analyze the period mod $m$ of a second order polynomially-recursive sequence. The problem originally comes from an enumeration of avoiding…

We prove a general theorem that gives a non trivial relation in the group of derived autoequivalences of a variety (or stack) X, under the assumption that there exists a suitable functor from the derived category of another variety Y…

We consider arbitrary bounded discrete time series originating from dynamical system with recursivity. More precisely, we provide an explicit construction of recurrent neural networks which effectively approximate the corresponding discrete…

Despite the many applications of rate-independent systems, their regularity theory is still largely unexplored. Usually, only weak solution with potentially very low regularity are considered, which requires non-smooth techniques. In this…

Let $A$ be a finite-dimensional algebra over an algebraically closed field. We prove $A$ is a strongly derived unbounded algebra if and only if there exists an integer $m$, such that $C_m(\proj A)$, the category of all minimal projective…

Denote by $\mathbb{N}$ and $\mathbb{P}$ the set of all positive integers and prime numbers, respectively. Let $\mathbb{P}=\{p_1<p_2<\dots <p_n<\dots\}$, where $p_n$ is the $n$-th prime number. For $k\in\mathbb{N}$ we recursively define…

A sequence of non-negative integers is called a B_k sequence if all the sums of arbitrary k elements are different. In this paper, we will present a new estimation for the upper bound of B_k sequences.

Trees or rooted trees have been generously studied in the literature. A forest is a set of trees or rooted trees. Here we give recurrence relations between the number of some kind of rooted forest with $k$ roots and that with $k+1$ roots on…

Tree-structured recursive neural networks (TreeRNNs) for sentence meaning have been successful for many applications, but it remains an open question whether the fixed-length representations that they learn can support tasks as demanding as…

Strong uniform Glivenko-Cantelli classes are weak uniform Glivenko-Cantelli, but to date results that prove the converse require additional conditions on the function class. This paper shows that no such extra requirements are necessary.

Many classification problems require decisions among a large number of competing classes. These tasks, however, are not handled well by general purpose learning methods and are usually addressed in an ad-hoc fashion. We suggest a general…

Given an action of a group $G$ by automorphisms on an infinite relational structure $\mathcal{M}$, we say that the action is structurally sharply $k$-transitive if, for any two $k$-tuples $\bar{a}, \bar{b} \in M^k$ of distinct elements such…

We determine the probability distribution for relative projective objects in an exceptional sequence of type $A_n$ of any length. We show that these events (the $j$-th object in an exceptional sequence of length $k\le n$ being relatively…

When a linear order has an order preserving surjection onto each of its suborders we say that it is strongly surjective. We prove that the set of countable strongly surjective linear orders is complete for the class of sets which are the…

In this paper we unify several existing regularity conditions for graphs, including strong regularity, $k$-isoregularity, and the $t$-vertex condition. We develop an algebraic composition/decomposition theory of regularity conditions. Using…

We study Bennett deep sequences in the context of recursion theory; in particular we investigate the notions of O(1)-deepK, O(1)-deepC , order-deep K and order-deep C sequences. Our main results are that Martin-Loef random sets are not…

A family of random matrices is said to converge strongly to a limiting family of operators if the operator norm of every noncommutative polynomial of the matrices converges to that of the limiting operators. Recent developments surrounding…

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…

A group word $w$ is said to be strongly concise in a class $\mathscr C$ of profinite groups if, for any group $G$ in $\mathscr C$, either $w$ takes at least continuum values in $G$ or the verbal subgroup $w(G)$ is finite. It is conjectured…