Related papers: A class of digit extraction BBP-type formulas in g…
We study the arithmetic circuit complexity of some well-known family of polynomials through the lens of parameterized complexity. Our main focus is on the construction of explicit algebraic branching programs (ABP) for determinant and…
We propose a new family of error detecting stabilizer codes with an encoding rate 1/3 that permit a transversal implementation of the pi/8-rotation $T$ on all logical qubits. The new codes are used to construct protocols for distilling…
We consider nested sums involving the Pochhammer symbol at infinity and rewrite them in terms of a small set of constants, such as powers of $\pi,$ $\log(2)$ or zeta values. In order to perform these simplifications, we view the series as…
By establishing an interesting connection between ordinary Bell polynomials and rational convolution powers, some composition and inverse relations of Bell polynomials as well as explicit expressions for convolution roots of sequences are…
Marginal polytopes are important geometric objects that arise in statistics as the polytopes underlying hierarchical log-linear models. These polytopes can be used to answer geometric questions about these models, such as determining the…
Legendre orthogonal moments have been widely used in the field of image analysis. Because their computation by a direct method is very time expensive, recent efforts have been devoted to the reduction of computational complexity.…
We adapt an old local-to-global technique of Ore to compute, under certain mild assumptions, an integral basis of a number field without a previous factorization of the discriminant of the defining polynomial. In a first phase, the method…
A new system of hexadecimal and base-256 numerals is proposed whose digit shapes are based on binary numerals. The proposed numerals are implemented in open source fonts and integrated into popular editors (Notepad++ and Eclipse) to prove…
In this paper we present applications of some special numbers obtained from a difference equation of degree three, especially in the Coding Theory. As a particular case, we obtain the generalized Pell-Fibonacci-Lucas numbers, which were…
We determine all pairs of positive integers $(a,b)$ such that $a+b$ and $a \times b$ have the same decimal digits in reverse order: \[ (2,2), (9,9), (3,24), (2,47), (2,497), (2,4997), (2,49997), \ldots \] We use deterministic finite…
Binary constant weight codes have important applications and have been studied for many years. Optimal or near-optimal binary constant weight codes of small lengths have been determined. In this paper we propose a new construction of…
In this paper we develop a very general class of bivariate discrete distributions. The basic idea is very simple. The marginals are obtained by taking the random geometric sum of a baseline distribution function. The proposed class of…
It is well known that all numbers that are normal of order $k$ in base $b$ are also normal of all orders less than $k$. Another basic fact is that every real number is normal in base $b$ if and only if it is simply normal in base $b^k$ for…
We obtained a new formula for $\pi$.
Summation-by-parts (SBP) operators are popular building blocks for systematically developing stable and high-order accurate numerical methods for time-dependent differential equations. The main idea behind existing SBP operators is that the…
Approximate Bayesian computation (ABC) or likelihood-free inference algorithms are used to find approximations to posterior distributions without making explicit use of the likelihood function, depending instead on simulation of sample data…
The mathematical constant pi has recently been computed up to 22,459,157,718,361 decimal and 18,651,926,753,033 hexadecimal digits. As a simple check for the normality of pi, the frequencies of all sequences with length one, two and three…
Although every exactly known bond percolation critical threshold is the root in $[0,1]$ of a lattice-dependent polynomial, it has recently been shown that the notion of a critical polynomial can be extended to any periodic lattice. The…
We show among others that the formula: $$ \lfloor n + \log_{\Phi}\{\sqrt{5}(\log_{\Phi}(\sqrt{5}n) + n) -5 + \frac{3}{n}\} - 2 \rfloor (n \geq 2), $$ (where $\Phi$ denotes the golden ratio and $\lfloor \rfloor$ denotes the integer part)…
Algebraic lattices are those obtained from modules in the ring of integers of algebraic number fields through the canonical or twisted embeddings. In turn, well-rounded lattices are those with maximal cardinality of linearly independent…