Related papers: Binary Prime Tableau Sequences
The well known prefer-one, prefer-opposite, and prefer-same binary de Bruijn sequences are all constructed using simple preference rules. We apply the technique of preference functions of span one to define q-ary sequences that generalize…
Preferential attachment graphs are random graphs designed to mimic properties of typical real world networks. They are constructed by a random process that iteratively adds vertices and attaches them preferentially to vertices that already…
New generalized cyclotomic binary sequences of period $p^2$ are proposed in this paper, where $p$ is an odd prime. The sequences are almost balanced and their linear complexity is determined. The result shows that the proposed sequences…
The pentagonal number theorem is extended to the sequence of the number of integer partitions with all parts equal. The new pentagonal number theorem implies that the distribution of the primes is just a specific detail of the application…
In this paper, for an odd prime $p$, several classes of two-weight linear codes over the finite field $\mathbb{F}_p$ are constructed from the defining sets, and then their complete weight distributions are determined by employing character…
We introduce a new privacy model relying on bistochastic matrices, that is, matrices whose components are nonnegative and sum to 1 both row-wise and column-wise. This class of matrices is used to both define privacy guarantees and a tool to…
By means of a binary visibility graph, we present a novel method to study random binary sequences. The behavior of the some topological properties of the binary visibility graph, such as the degree distribution, the clustering coefficient,…
In this paper, we study the problem of summation evaluation of secrets. The secrets are distributed over a network of nodes that form a ring graph. Privacy-preserving iterative protocols for computing the sum of the secrets are proposed,…
This paper presents a distinctive prime detection approach. This method use GM-(n+1) sequences to effectively eliminate complex numbers. The sequences, which consist of odd a number of (n+1), exclude all components except for the initial…
Finite dimensional simple modules of quantum affine algebras of type A correspond to semistandard Young tableaux of rectangular shapes. In this paper, we classify all prime modules corresponding to 2-column semistandard Young tableaux, up…
Binary sequences with good autocorrelation properties and large linear complexity are useful in stream cipher cryptography. The Sidelnikov-Lempel-Cohn-Eastman (SLCE) sequences have nearly optimal autocorrelation. However, the problem of…
We suggest other models of sieve generated sequences like the Sieve of Eratosthenes to explain randomness properties of the prime numbers, like the twin prime conjecture, the lim sup conjecture, the Riemann conjecture, and the prime number…
We describe an algorithm for the sequential sampling of entries in multiway contingency tables with given constraints. The algorithm can be used for computations in exact conditional inference. To justify the algorithm, a theory relates…
This work proposes a novel adaptation of a pretrained sequence-to-sequence model to the task of document ranking. Our approach is fundamentally different from a commonly-adopted classification-based formulation of ranking, based on…
The extent to which a sequence of finite length differs from a shifted version of itself is measured by its aperiodic autocorrelations. Of particular interest are sequences whose entries are 1 or -1, called binary sequences, and sequences…
We give the trace representation of a family of binary sequences derived from Euler quotients by determining the corresponding defining polynomials. Trace representation can help us producing the sequences efficiently and analyzing their…
Pseudorandom sequences are used extensively in communications and remote sensing. Correlation provides one measure of pseudorandomness, and low correlation is an important factor determining the performance of digital sequences in…
Motivated by the problem of reducing the peak to average power ratio (PAPR) of transmitted signals, we consider a design of complementary set matrices whose column sequences satisfy a correlation constraint. The design algorithm recursively…
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…
We look at a family of meta-Fibonacci sequences which arise in studying the number of leaves at the largest level in certain infinite sequences of binary trees, restricted compositions of an integer, and binary compact codes. For this…