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An array is a "list of lists" with the length of each level of list the same. The size (sometimes called the "shape") of a d-dimensional array is then indicated as ...

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 ...

Minkowski's conjecture states that every lattice tiling of R^n by unit hypercubes contains two hypercubes that meet in an (n-1)-dimensional face. Minkowski first considered ...

Find a way to stack a square of cannonballs laid out on the ground into a square pyramid (i.e., find a square number which is also square pyramidal). This corresponds to ...

A heterosquare is an n×n array of the integers from 1 to n^2 such that the rows, columns, and diagonals have different sums. (By contrast, in a magic square, they have the ...

For every positive integer n, there exists a square in the plane with exactly n lattice points in its interior. This was extended by Schinzel and Kulikowski to all plane ...

A cylinder can be dissected into unequal squares, with nine squares required at a minimum. Trivial squarings can be constructed by taking rectangle dissections and matching ...

The area of a rational right triangle cannot be a square number. This statement is equivalent to "a congruum cannot be a square number."

The order n>=2 L-polyomino consists of a vertical line of n squares with a single additional square attached at the bottom.

There are two equivalent definitions for a nilpotent matrix. 1. A square matrix whose eigenvalues are all 0. 2. A square matrix A such that A^n is the zero matrix 0 for some ...