An incidence structure is something quite simple: a pair of sets A, B and some relation, represented as a subset I contained in AxB. This is a  useful tool to describe finite geometric and combinatorial objects in a general fashion.  For  an incidence structure one defines an incidence matrix M, with  rows  indexed by  A and columns  indexed by B, so that the (a,b)-entry of  M  is =1 if and only if  (a,b) belongs to I, and =0 otherwise.

The  Smith normal form of M contains important information about the structure. Usually this normal form is very difficult to determine and it is known only for few standard combinatorial objects. In this project we want to look at this question for finite projective spaces.

Further information about this topic can be found in [1]  [2] and [3].

This project is also open to any applicant (home, EU or Overseas) who have their own funding. 

F. Dalla Volta,  J. Siemons, The Smith form of Incidence maps and Eigenspace Decompositions, Journal of Combinatorial Theory Ser. A, to appear.

R.M Wilson, J. van Lint, A Course in Combinatorics, CUP 1996

Codes and modules associated with designs and t-uniform hypergraphs, Richard M. Wilson, NATO ASI, 2006