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A pentomino is a 5-polyomino. There are 12 free pentominoes, 18 one-sided pentominoes, and 63 fixed pentominoes. The twelve free pentominoes are known by the letters of the ...

Perspective is the art and mathematics of realistically depicting three-dimensional objects in a two-dimensional plane, sometimes called centric or natural perspective to ...

Three-dimensional generalization of the polyominoes to n dimensions. The number of polycubes N(n) composed of n cubes are 1, 1, 2, 8, 29, 166, 1023, ... (OEIS A000162; Ball ...

For every positive integer n, there exists a circle in the plane having exactly n lattice points on its circumference. The theorem is based on the number r(n) of integral ...

The space groups in two dimensions are called wallpaper groups. In three dimensions, the space groups are the symmetry groups possible in a crystal lattice with the ...

Let L be a finite-dimensional split semisimple Lie algebra over a field of field characteristic 0, H a splitting Cartan subalgebra, and Lambda a weight of H in a ...

Let P be a finite partially ordered set, then an antichain in P is a set of pairwise incomparable elements. Antichains are also called Sperner systems in older literature ...

The McLaughlin graph is a 112-regular graph on 275 nodes and 15400 edges that can be constructed from the Witt design. It is distance-regular with intersection array ...

The inequality (j+1)a_j+a_i>=(j+1)i, which is satisfied by all A-sequences.

A geometric sequence is a sequence {a_k}, k=0, 1, ..., such that each term is given by a multiple r of the previous one. Another equivalent definition is that a sequence is ...