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A pair of dice which have the same odds for throwing every number as a normal pair of 6-sided dice. They are the only such alternate arrangement if face values are required ...

Let a simple graph G have n vertices, chromatic polynomial P(x), and chromatic number chi. Then P(G) can be written as P(G)=sum_(i=0)^ha_i·(x)_(p-i), where h=n-chi and (x)_k ...

The number of operations needed to effect a geometric construction as determined in geometrography. If the number of operations of the five geometrographic types are denoted ...

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 ...

The usual number of scalar operations (i.e., the total number of additions and multiplications) required to perform n×n matrix multiplication is M(n)=2n^3-n^2 (1) (i.e., n^3 ...

In the early 1960s, B. Birch and H. P. F. Swinnerton-Dyer conjectured that if a given elliptic curve has an infinite number of solutions, then the associated L-series has ...

P. G. Tait undertook a study of knots in response to Kelvin's conjecture that the atoms were composed of knotted vortex tubes of ether (Thomson 1869). He categorized knots in ...

There are a number of hypotraceable and hypohamiltonian graphs associated with Carsten Thomassen. These graphs, illustrated above, are implemented in the Wolfram Language as ...

Triangulation is the division of a surface or plane polygon into a set of triangles, usually with the restriction that each triangle side is entirely shared by two adjacent ...