## The invariant factors of the incidence matrices of points and subspaces in $\operatorname {PG}(n,q)$ and $\operatorname {AG}(n,q)$

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- by David B. Chandler, Peter Sin and Qing Xiang PDF
- Trans. Amer. Math. Soc.
**358**(2006), 4935-4957 Request permission

## Abstract:

We determine the Smith normal forms of the incidence matrices of points and projective $(r-1)$-dimensional subspaces of $\operatorname {PG}(n,q)$ and of the incidence matrices of points and $r$-dimensional affine subspaces of $\operatorname {AG}(n,q)$ for all $n$, $r$, and arbitrary prime power $q$.## References

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## Additional Information

**David B. Chandler**- Affiliation: Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716
- Address at time of publication: Institute of Mathematics, Academia Sinica, NanGang, Taipei 11529, Taiwan
- Email: chandler@math.udel.edu
**Peter Sin**- Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611
- Email: sin@math.ufl.edu
**Qing Xiang**- Affiliation: Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716
- Email: xiang@math.udel.edu
- Received by editor(s): April 27, 2004
- Received by editor(s) in revised form: September 27, 2004
- Published electronically: April 11, 2006
- Additional Notes: The second author was partially supported by NSF grant DMS-0071060. The third author was partially supported by NSA grant MDA904-01-1-0036.
- © Copyright 2006
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc.
**358**(2006), 4935-4957 - MSC (2000): Primary 05E20; Secondary 20G05, 20C11
- DOI: https://doi.org/10.1090/S0002-9947-06-03859-1
- MathSciNet review: 2231879