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The Ionin-Kharaghani graph is a strongly regular graph on 765 vertices and 73440 edges. It has regular parameters (nu,k,lambda,mu)=(765,192,48,48). It is implemented in the ...

Two groups are isomorphic if the correspondence between them is one-to-one and the "multiplication" table is preserved. For example, the point groups C_2 and D_1 are ...

The dimension d of any irreducible representation of a group G must be a divisor of the index of each maximal normal Abelian subgroup of G. Note that while Itô's theorem was ...

Every finite-dimensional Lie algebra of characteristic p!=0 has a faithful finite-dimensional representation.

Given a convex plane region with area A and perimeter p, then |N-A|<p, where N is the number of enclosed lattice points.

The circumcircle of the Johnson triangle DeltaJ_AJ_BJ_C has center at the orthocenter H of the reference triangle and radius R, where R is the circumradius of the reference ...

A transformation of an algebraic curve which is of the same type as its inverse. A Jonquière's transformation is always factorable.

Let V!=(0) be a finite dimensional vector space over the complex numbers, and let A be a linear operator on V. Then V can be expressed as a direct sum of cyclic subspaces.

In Kepler's 1619 book Harmonice Mundi on tilings, he discussed a tiling built with pentagons, pentagrams, decagons, and "fused decagon pairs." He also called them "monsters." ...

Let the center B of a circle of radius a move along a line BA. Let O be a fixed point located a distance c away from AB. Draw a secant line through O and D, the midpoint of ...