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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.

3 votes
1 answer
147 views

Mutually orthogonal Latin hypercubes

A $d$-dimensional Latin hypercube with side length $n$ is a $d$-dimensional array with $n$ symbols such that along any line parallel to an axis, each symbol appears exactly once. Let us call a $(n,d)$ …
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  • 675
8 votes
1 answer
203 views

Sets of residues with only a single intersection under translation

A combinatorial game I am studying has given rise to the following question. Consider the group $\Bbb Z/n\Bbb Z$. What is the largest $m$ such that there exist $k$ sets of $m$ residues such that the i …
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  • 675
15 votes

Examples of errors in computational combinatorics results

About 20 years ago, the number of groups of order 1024 was reported to be 49487365422 in "A millennium project: constructing small groups", and this number was repeated in other sources. Recently, Bur …