Combinatorics / CONCEPT

Component parity of uniform reflection arrays

Fix one indexed array of 2n permutation rows on n columns and n symbols. Fibres and joint counts refer to this same array and its original row indices. For odd n at least three, fibre size two and equality of reflected joint counts force its fibre graph to be connected. The conclusion also applies to arrays whose first row is the identity and whose rows are sorted on their original labels.