Related papers: Efficient Generation of Binary Magic Squares
Some techniques for the use of bitwise operations are described in the article. As an example, an open problem of isomorphism-free generations of combinatorial objects is discussed. An equivalence relation on the set of square binary…
Multiple binomial sums form a large class of multi-indexed sequences, closed under partial summation, which contains most of the sequences obtained by multiple summation of products of binomial coefficients and also all the sequences with…
A magic rectangle of order $m\times n$ with precisely $r$ filled cells in each row and precisely $s$ filled cells in each column, denoted $MR(m,n;r,s)$, is an arrangement of the numbers from 0 to $mr-1$ in an $m\times n$ array such that…
Ouroboros functions have shown some interesting properties when subjected to conventional operations. The aim of this paper is to continue our investigation and prove some additional properties of these functions. Using algebraic methods,…
Despite the rapidly evolving field of computational electromagnetics, few open-source tools have managed to tackle the problem of automatic mesh generation for properly discretizing the problem of interest into a finite set of elements…
We present an algorithm for effectively generating binary sequences which would be rated by people as highly likely to have been generated by a random process, such as flipping a fair coin.
This note describes a technique for generating large non-singular matrices with blocks of full rank. Our motivation to construct such matrices arises in the white-box implementation of cryptographic algorithms with S-boxes.
In this short paper we have produced different kinds of upside down magic squares based on a palindromic day 11.02.2011. In this day appear only the algorisms 0, 1 and 2. Some of the magic squares are bimagic and some are palindromic. Magic…
We propose efficient algorithms for enumerating maximal common subsequences (MCSs) of two strings. Efficiency of the algorithms are estimated by the preprocessing-time, space, and delay-time complexities. One algorithm prepares a…
We re-examine previous constructions of infinite binary words containing few distinct squares with the goal of finding the "simplest", in a certain sense. We exhibit several new constructions. Rather than using tedious case-based arguments…
In this paper we have produced different kinds of bimagic squares based on bimagic squares of order 8x8, 16x16, 25x25, 49x49, etc. A different technique is applied to produce bimagic square of order 16x16, 25x25, 49x49, etc. The bimagic…
In this paper we give the first method for constructing n-multimagic squares (and hypercubes) for any n. We give an explicit formula in the case of squares and an effective existence proof in the higher dimensional case. Finally we prove…
This article looks at the eigenvalues of magic squares generated by the MATLAB's magic($n$) function. The magic($n$) function constructs doubly even ($n = 4k$) magic squares, singly even ($n = 4k+2$) magic squares and odd ($n = 2k+1$) magic…
Variational quantum algorithms (VQAs) offer a promising near-term approach to finding optimal quantum strategies for playing non-local games. These games test quantum correlations beyond classical limits and enable entanglement…
We propose geometrical methods for constructing square 01-matrices with the same number n of units in every row and column, and such that any two rows of the matrix contain at most one unit in common. These matrices are equivalent to…
Using computational algebraic geometry techniques and Hilbert bases of polyhedral cones we derive explicit formulas and generating functions for the number of magic squares and magic cubes.
We review a known method of compounding two magic square matrices of order m and n with the all-ones matrix to form two magic square matrices of order mn. We show that these compounded matrices commute. Simple formulas are derived for their…
We present a randomized algorithm, which, given positive integers n and t and a real number 0< epsilon <1, computes the number Sigma(n, t) of n x n non-negative integer matrices (magic squares) with the row and column sums equal to t within…
We describe three algorithms for generating binary-valued holograms. Our methods are optimised for producing large arrays of tightly focussed optical tweezers for trapping particles. Binary-valued holograms allow us to use a digital mirror…
In standard clustering problems, data points are represented by vectors, and by stacking them together, one forms a data matrix with row or column cluster structure. In this paper, we consider a class of binary matrices, arising in many…