  The purpose of this note is to exhibit clearly how the "graphical
condensation" identities of Kuo, Yan, Yeh and Zhang follow from classical
Pfaffian identities by the Kasteleyn-Percus method for the enumeration of
matchings. Knuth termed the relevant identities "overlapping Pfaffian"
identities and the key concept of proof "superpositions of matchings". In our
uniform presentation of the material, we also give an apparently unpublished
general "overlapping Pfaffian" identity of Krattenthaler.
  A previous version of this paper contained an erroneous application of the
Kasteleyn-Percus method, which is now corrected.

Combinatorics