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One would think that by analogy with the matching-generating polynomial, independence polynomial, etc., a path polynomial whose coefficients are the numbers of paths of ...

The numerators and denominators obtained by taking the ratios of adjacent terms in the triangular array of the number of +1 "bordered" alternating sign matrices A_n with a 1 ...

Strang's strange figures are the figures produced by plotting a periodic function f(z) as a function of an integer argument n for n=1, 2, .... Unexpected patterns and ...

In nonstandard analysis, the limitation to first-order analysis can be avoided by using a construction known as a superstructure. Superstructures are constructed in the ...

A recursive function devised by I. Takeuchi in 1978 (Knuth 1998). For integers x, y, and z, it is defined by (1) This can be described more simply by t(x,y,z)={y if x<=y; {z ...

A number of four-tetrahedron compounds can be constructed by rotating about the center-centroid lines of each face. Three such compounds are shown above for rotations by ...

Let n be a positive number having primitive roots. If g is a primitive root of n, then the numbers 1, g, g^2, ..., g^(phi(n)-1) form a reduced residue system modulo n, where ...

The beautiful arrangement of leaves in some plants, called phyllotaxis, obeys a number of subtle mathematical relationships. For instance, the florets in the head of a ...

The Greenfield graph is the name given in this work to the 12-vertex graph illustrated above due to Greenfield (2011). This graph provided the first known example which ...

Find the maximum number of bishops B(n) that can be placed on an n×n chessboard such that no two attack each other. The answer is 2n-2 (Dudeney 1970, Madachy 1979), giving ...