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The polynomials G_n(x;a,b) given by the associated Sheffer sequence with f(t)=e^(at)(e^(bt)-1), (1) where b!=0. The inverse function (and therefore generating function) ...

Consider an n×n (0, 1)-matrix such as [a_(11) a_(23) ; a_(22) a_(34); a_(21) a_(33) ; a_(32) a_(44); a_(31) a_(43) ; a_(42) a_(54); a_(41) a_(53) ; a_(52) a_(64)] (1) for ...

There are a number of tilings of various shapes by all the 12 order n=6 polyiamonds, summarized in the following table. Several of these (starred in the table below) are also ...

There are (at least) two graphs associated with Horton, illustrated above. The first is a graph on 96 nodes providing a counterexample to the Tutte conjecture that every ...

The Johnson solids are the convex polyhedra having regular faces and equal edge lengths (with the exception of the completely regular Platonic solids, the "semiregular" ...

An integer j(n) is called a jumping champion if j(n) is the most frequently occurring difference between consecutive primes <=n (Odlyzko et al. 1999). This term was coined by ...

The Kronecker-Weber theorem, sometimes known as the Kronecker-Weber-Hilbert theorem, is one of the earliest known results in class field theory. In layman's terms, the ...

Cubic lattice sums include the following: b_2(2s) = sum^'_(i,j=-infty)^infty((-1)^(i+j))/((i^2+j^2)^s) (1) b_3(2s) = ...

A short theorem used in proving a larger theorem. Related concepts are the axiom, porism, postulate, principle, and theorem. The late mathematician P. Erdős has often been ...

A (general) octahedron is a polyhedron having eight faces. Examples include the 4-trapezohedron, augmented triangular prism (Johnson solid J_(49)), bislit cube, Dürer solid, ...