Search Results for ""

A sparse matrix is a matrix that allows special techniques to take advantage of the large number of "background" (commonly zero) elements. The number of zeros a matrix needs ...

A stack polyomino is a self-avoiding convex polyomino containing two adjacent corners of its minimal bounding rectangle. The number of stack polyominoes with perimeter 2n+4 ...

Van der Corput sequences are a means of generating sequences of points that are maximally self-avoiding (a.k.a. quasirandom sequences). In the one-dimensional case, the ...

A formula for the Bell polynomial and Bell numbers. The general formula states that B_n(x)=e^(-x)sum_(k=0)^infty(k^n)/(k!)x^k, (1) where B_n(x) is a Bell polynomial (Roman ...

The Golomb graph is a unit-distance graph discovered around 1960-1965 by Golomb (Soifer 2008, p. 19). It is implemented in the Wolfram Language as GraphData["GolombGraph"]. A ...

A lossless data compression algorithm which uses a small number of bits to encode common characters. Huffman coding approximates the probability for each character as a power ...

The Parts graphs are a set of unit-distance graphs with chromatic number five derived by Jaan Parts in 2019-2020 (Parts 2020a). They provide some of the smallest known ...

The Pell graph Pi_n is the graph defined as follows. Consider n-tuples of (0,1,2) such that maximal blocks of an odd number of 2's are forbidden. Take these as the vertices ...

Wang's conjecture states that if a set of tiles can tile the plane, then they can always be arranged to do so periodically (Wang 1961). The conjecture was refuted when Berger ...

An independent vertex set of a graph G is a subset of the vertices such that no two vertices in the subset represent an edge of G. The figure above shows independent sets ...