Related papers: Almost p-ary Sequences

Perfect complementary sequence sets (PCSSs) are widely used in multi-carrier code-division multiple-access (MC-CDMA) communication systems. However, the set size of a PCSS is upper bounded by the number of row sequences of each…

We present conjectures for the space-time form and leading large N dependence of extremal and near-extremal correlation functions in the \N=8 superconformal Yang-Mills theory in d=3 as well as in the (0,2) superconformal theory in d=6,…

Let $\mathcal{A}$ and $\matchcal{B}$ denote two families of subsets of an $n$-element set. The pair $(\mathcal{A},\mathcal{B})$ is said to be $\ell$-cross-intersecting iff $|A\cap B| = \ell$ for all $A\in\mathcal{A}$ and $B\in\mathcal{B}$.…

We consider the problem of finding maximal sets of shift-inequivalent decimations of Sidelnikov-Lempel-Cohn-Eastman (SLCE) sequences (as well as the equivalent problem of determining the multiplier groups of the almost difference sets…

We give a formula relating the topological rank of the full group of an aperiodic pmp equivalence relation to the cost of its ergodic components. Furthermore, we obtain examples of full groups having a dense free subgroup whose rank is…

Using a sieve-theoretic argument, we show that almost all gaps $(p_n, p_{n+1})$ between consecutive primes $p_n, p_{n+1}$ contain a natural number $m$ whose least prime factor $p(m)$ is at least the length $p_{n+1} - p_n$ of the gap,…

Binary periodic sequences with good autocorrelation property have many applications in many aspects of communication. In past decades many series of such binary sequences have been constructed. In the application of cryptography, such…

We study discrete Schroedinger operators with analytic potentials. In particular, we are interested in the connection between the absolutely continuous spectrum in the almost periodic case and the spectra in the periodic case. We prove a…

A subset $S\subseteq V$ in a graph $G=(V,E)$ is a $k$-quasiperfect dominating set (for $k\geq 1$) if every vertex not in $S$ is adjacent to at least one and at most $k$ vertices in $S$. The cardinality of a minimum $k$-quasiperfect…

We describe completely conformal Killing or conformal Killing-Yano (CKY) $p$-forms on almost abelian metric Lie algebras. In particular we prove that if a $n$-dimensional almost abelian metric Lie algebra admits a non-parallel CKY $p$-form,…

A graph $G$ on $n$ vertices is \textit{pancyclic} if it contains cycles of length $t$ for all $3 \leq t \leq n$. In this paper we prove that for any fixed $\epsilon>0$, the random graph $G(n,p)$ with $p(n)\gg n^{-1/2}$ asymptotically almost…

We investigate a family of regression problems in a semi-supervised setting. The task is to assign real-valued labels to a set of $n$ sample points, provided a small training subset of $N$ labeled points. A goal of semi-supervised learning…

In this paper, we study some supercongruences involving the sequence $$ t_n(x)=\sum_{k=0}^n\binom{n}{k}\binom{x}{k}\binom{x+k}{k}2^k $$ and solve some open problems. For any odd prime $p$ and $p$-adic integer $x$, we determine…

We study some notions of cohomology for asymptotically additive sequences and prove a Liv\v{s}ic-type result for almost additive sequences of potentials. As a consequence, we are able to characterize almost additive sequences based on their…

We introduce a construction for perfect periodic autocorrelation sequences over roots of unity. The sequences share similarities to the perfect periodic sequence constructions of Liu, Frank, and Milewski.

For a prime $p\ge 5$ let $q_0,q_1,\ldots,q_{(p-3)/2}$ be the quadratic residues modulo $p$ in increasing order. We study two $(p-3)/2$-periodic binary sequences $(d_n)$ and $(t_n)$ defined by $d_n=q_n+q_{n+1}\bmod 2$ and $t_n=1$ if…

We study for each fixed integer $g \ge 2$, for all primes $\ell$ and $p$ with $\ell \neq p$, finite regular directed graphs associated with the set of equivalence classes of $\ell$-marked principally polarized superspecial abelian varieties…

A sequence $\mathbf{A}$ is said to be realizable if satisfies so called sign and Dold conditions. We will say that a sequence almost satisfies the Dold condition if there exists a constant $c\in\mathbb{N}_+$ such that…

We examine the linear complexity and the autocorrelation properties of new quaternary cyclotomic sequences of period 2p. The sequences are constructed via the cyclotomic classes of order four.

Given a sequence of complex square matrices, $a_n$, consider the sequence of their partial products, defined by $p_n=p_{n-1}a_{n}$. What can be said about the asymptotics as $n\to\infty$ of the sequence $f(p_n)$, where $f$ is a continuous…