Tactical decomposition of incidence structure

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This term is related to: incidence geometry
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Definition

A tactical decomposition of an incidence structure is the following data:

  • A partition of the point set into point classes
  • A partition of the block set into block classes

such that the induced incidence structure on any pair of point class and block class is a tactical configuration.

Given any tactical decomposition, we can also associate a quotient structure by that tactical decomposition.