There is a way of grouping elements into (more than one) equal-sized blocks such that no block appears twice vs. there exists no such grouping.

There is a way of grouping elements into (more than one) equal-sized blocks such that no block is used twice vs. there exists no such grouping.

Sequences with a prime number of elements are sorted left when all their elements are unique, and sorted right otherwise.

The sequence ABBABB would be sorted left, as it could be grouped into (AB)(BA)(BB), where each block is unique.

Leo Crabbe