Related papers: A special class of pure $O$-sequences

In this article one builds a class of recursive sets, one establishes properties of these sets, and one proposes applications.

This paper presents a class of random orthogonal sequences associated with the number theoretic Hilbert transform. We present a constructive procedure for finding the random sequences for different modulus values. These random sequences…

In this paper we get two new classes of regular sequences in the polynomial ring over the field of complex numbers.

We study structure of pure morphic and morphic sequences and prove the following result: the subword complexity of arbitrary morphic sequence is either $\Theta(n^{1+1/k})$ for some $k\in\mathbb N$, or is $O(n \log n)$.

Necessary and sufficient conditions for a sequence of positive integers to be the degree sequence of a k-connected simple graph are detailed. Conditions are also given under which such a sequence is necessarily k-connected.

This paper establishes new restrictions for attainable enhanced principal rank characteristic sequences (epr-sequences). These results are then used to classify two related families of sequences that are attainable by a real symmetric…

In the present paper we obtain the list of algebras, up to isomorphism, such that closure of any complex finite-dimensional algebra contains one of the algebra of the given list.

We investigate maximal exceptional sequences of line bundles on (P^1)^3, i.e. those consisting of 2^r elements. For r=3 we show that they are always full, meaning that they generate the derived category. Everything is done in the discrete…

We count the number of subsets of $\{1,2,\cdots,n\}$ under different conditions and study the sequence obtained as we let $n$ increase.

For any $n$ and $k$, we provide an explicit (that is, computable in polynomial time) example of integer $B_k$-sequence of size $n$ consisting of elements bounded by $n^{k+o(k)}$.

In this note we provide a simple formula of general term of recurrent sequence.

We study tangent sets of strictly self-affine sets in the plane. If a set in this class satisfies the strong separation condition and projects to a line segment for sufficiently many directions, then for each generic point there exists a…

In this paper, we give a class of reconstructible graphs.

We define a proper differential sequence of ordinary differential equations and introduce a method to derive an alternative sequence of integrals for such a sequence. We describe some general properties which are illustrated by several…

The Kolakoski sequence is the unique infinite sequence with values in $\{1, 2\}$ and first term twems $1, 2, \ldots$ which equals the sequence of run-lengths of itself, we call this $K(1, 2).$ We define $K(m, n)$ similarly for $m+n$ odd. A…

We show that the $Kn$--smooth part of $a^n-1$ for an integer $a>1$ is $a^{o(n)}$ for most positive integers $n$.

P(n,s) denotes the number of permutations of 1,2,...n that have exactly s sequences. Canfield and Wilf [math.CO/0609704] recently showed that P(n,s) can be written as a sum of s polynomials in n. We determine these polynomials explicitly…

We describe two types of localization for $(\infty, 1)$-categories which determine the successive terms in the homotopy spectral sequence of a (co)simplicial object.

Morphic sequences form a natural class of infinite sequences, typically defined as the coding of a fixed point of a morphism. Different morphisms and codings may yield the same morphic sequence. This paper investigates how to prove that two…

We explain how to set up the homotopy spectral sequence of a (co)simplicial object in an $\infty$-category, with an emphasis on how to construct the differentials in a model-invariant manner.