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There are a number of attractive polyhedron compounds consisting of five octahedra. The first octahedron 5-compound is a polyhedron compound composed of five octahedra ...

The pentakis dodecahedral graph is Archimedean dual graph which is the skeleton of the disdyakis triacontahedron. It is implemented in the Wolfram Language as ...

A polyomino tiling is a tiling of the plane by specified types of polyominoes. Tiling by polyominoes has been investigated since at least the late 1950s, particularly by S. ...

Pronic numbers are figurate numbers of the form P_n=2T_n=n(n+1), where T_n is the nth triangular number. The first few are 2, 6, 12, 20, 30, 42, 56, 72, 90, 110, ... (OEIS ...

Find two distinct sets of integers {a_1,...,a_n} and {b_1,...,b_n}, such that for k=1, ..., m, sum_(i=1)^na_i^k=sum_(i=1)^nb_i^k. (1) The Prouhet-Tarry-Escott problem is ...

A notion introduced by R. M. Wilson in 1974. Given a finite graph G with n vertices, puz(G) is defined as the graph whose nodes are the labelings of G leaving one node ...

The quadratic embedding constant QEC(G) of a finite simple connected graph G on n vertices is defined as the maximum of the product vDv over all real n-vectors v satisfying ...

The word quadrature has (at least) three incompatible meanings. Integration by quadrature either means solving an integral analytically (i.e., symbolically in terms of known ...

The rank polynomial R(x,y) of a general graph G is the function defined by R(x,y)=sum_(S subset= E(G))x^(r(S))y^(s(S)), (1) where the sum is taken over all subgraphs (i.e., ...

Any square matrix T has a canonical form without any need to extend the field of its coefficients. For instance, if the entries of T are rational numbers, then so are the ...