Transactions of the American Mathematical Society

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

Author(s): David B. Chandler; Peter Sin; Qing Xiang
Journal: Trans. Amer. Math. Soc. 358 (2006), 4935-4957.
MSC (2000): Primary 05E20; Secondary 20G05, 20C11
Posted: April 11, 2006
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Abstract: We determine the Smith normal forms of the incidence matrices of points and projective

-dimensional subspaces of $\operatorname{PG}(n,q)$ and of the incidence matrices of points and

-dimensional affine subspaces of $\operatorname{AG}(n,q)$ for all

, and arbitrary prime power

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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

DOI: 10.1090/S0002-9947-06-03859-1
PII: S 0002-9947(06)03859-1
Received by editor(s): April 27, 2004
Received by editor(s) in revised form: September 27, 2004
Posted: 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 of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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