The usual quantum logic, beginning with Birkhoff and Von Neumann, was the logic of closed subspaces of a Hilbert space. This paper develops the more general logic of direct-sum decompositions of a vector space. This allows the treatment of measurement of any self-adjoint operators rather than just the projection operators associated with subspaces.

## Counting Direct-sum Decompositions

March 28, 2016 by

This paper uses elementary methods to derive the formulas for and to tablulate (in the case q = 2) two related q-analogs of the Stirling numbers of the second kind and the Bell numbers for direct-sum decompositions (vector space analogs of set partitions) of a finite vector space over a finite field with q elements.