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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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


Authors: David B. Chandler, Peter Sin and Qing Xiang
Journal: Trans. Amer. Math. Soc. 358 (2006), 4935-4957
MSC (2000): Primary 05E20; Secondary 20G05, 20C11
Published electronically: April 11, 2006
MathSciNet review: 2231879
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Abstract | References | Similar Articles | Additional Information

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$.


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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

DOI: http://dx.doi.org/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
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.
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.