Distance matrices of subsets of the Hamming cube

Graham and Winkler derived a formula for the determinant of distance matrix full-dimensional set n + 1 points { x 0 , … } in Hamming cube H = ( ? ) . In this article we derive D an arbitrary m It follows from more general that det ? if only vectors are affinely independent. Specializing to case provides new insights into original Winkler. A significant difference arises between cases < is noted. We also show unweighted tree on vertices, then ? ? ? 2 ? where column vector all whose coordinates 1. Finally, proof Murugan’s classification subsets have strict 1-negative type.