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A figurate number which is constructed as an octahedral number with a square pyramid removed from each of the six graph vertices, TO_n = O_(3n-2)-6P_(n-1)^((4)) (1) = ...

The word weight has many uses in mathematics. It can refer to a function w(x) (also called a weighting function or weighting function) used to normalize orthogonal functions. ...

C_4 is one of the two groups of group order 4. Like C_2×C_2, it is Abelian, but unlike C_2×C_2, it is a cyclic. Examples include the point groups C_4 (note that the same ...

A modulo multiplication group is a finite group M_m of residue classes prime to m under multiplication mod m. M_m is Abelian of group order phi(m), where phi(m) is the ...

A base-60, or sexagesimal, number system, used by the ancient Babylonians.

A 4-sphere has positive curvature, with R^2=x^2+y^2+z^2+w^2 (1) 2x(dx)/(dw)+2y(dy)/(dw)+2z(dz)/(dw)+2w=0. (2) Since r=xx^^+yy^^+zz^^ (3) dw = -(xdx+ydy+zdz)/w (4) = ...

Betti numbers are topological objects which were proved to be invariants by Poincaré, and used by him to extend the polyhedral formula to higher dimensional spaces. ...

The dihedral group D_3 is a particular instance of one of the two distinct abstract groups of group order 6. Unlike the cyclic group C_6 (which is Abelian), D_3 is ...

A fusene is a simple planar 2-connected graph embedded in the plane with all vertices of degree 2 or 3, all bounded faces (not necessarily regular) hexagons, and all vertices ...

For an integer n>=2, let lpf(n) denote the least prime factor of n. A pair of integers (x,y) is called a twin peak if 1. x<y, 2. lpf(x)=lpf(y), 3. For all z, x<z<y implies ...