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The elementary divisors of the incidence matrix of skew lines in $ \mathrm{PG}(3,q)$


Authors: Andries E. Brouwer, Joshua E. Ducey and Peter Sin
Journal: Proc. Amer. Math. Soc. 140 (2012), 2561-2573
MSC (2010): Primary 05B20; Secondary 20C33, 51E20
DOI: https://doi.org/10.1090/S0002-9939-2011-11462-X
Published electronically: December 21, 2011
MathSciNet review: 2910745
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Abstract: The elementary divisors of the incidence matrix of lines in $ \operatorname {PG}(3,q)$ are computed, where two lines are incident if and only if they are skew.


References [Enhancements On Off] (What's this?)

  • 1. Matthew Bardoe and Peter Sin, The permutation modules for $ {\rm GL}(n+1,{\bf F}_q)$ acting on $ {\bf P}^n({\bf F}_q)$ and $ {\bf F}^{n-1}_q$, J. London Math. Soc. (2) 61 (2000), no. 1, 58-80. MR 1745400 (2001f:20103)
  • 2. David B. Chandler, Peter Sin, and Qing Xiang, The invariant factors of the incidence matrices of points and subspaces in $ {\rm PG}(n,q)$ and $ {\rm AG}(n,q)$, Trans. Amer. Math. Soc. 358 (2006), no. 11, 4935-4957 (electronic). MR 2231879 (2007c:05041)
  • 3. Noboru Hamada, On the $ p$-rank of the incidence matrix of a balanced or partially balanced incomplete block design and its applications to error correcting codes, Hiroshima Math. J. 3 (1973), 153-226. MR 0332515 (48:10842)
  • 4. Eric S. Lander, Symmetric designs: An algebraic approach, London Math. Soc. Lecture Notes 74. Cambridge University Press, 1983. MR 697566 (85d:05041)
  • 5. Joseph John Rushanan, Topics in integral matrices and abelian group codes, Thesis (Ph.D.)-California Institute of Technology, 1986, ProQuest LLC, Ann Arbor, MI. MR 2635072
  • 6. Peter Sin, The elementary divisors of the incidence matrices of points and linear subspaces in $ \mathbf P^n(\mathbf F_p)$, J. Algebra 232 (2000), no. 1, 76-85. MR 1783914 (2001g:20060)
  • 7. -, The $ p$-rank of the incidence matrix of intersecting linear subspaces, Des. Codes Cryptogr. 31 (2004), no. 3, 213-220. MR 2047880 (2004m:05050)
  • 8. Qing Xiang, Recent progress in algebraic design theory, Finite Fields Appl. 11 (2005), no. 3, 622-653. MR 2158779 (2006j:05001)
  • 9. -, Recent results on $ p$-ranks and Smith normal forms of some $ 2$$ \text {-}(v,k,\lambda )$ designs, Coding theory and quantum computing, Contemp. Math., vol. 381, Amer. Math. Soc., Providence, RI, 2005, pp. 53-67. MR 2170799 (2006h:05035)

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Additional Information

Andries E. Brouwer
Affiliation: Department of Mathematics, Technische Universiteit Eindhoven, 5600MB Eindhoven, The Netherlands
Email: aeb@cwi.nl

Joshua E. Ducey
Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611–8105
Address at time of publication: Department of Mathematics and Statistics, James Madison University, Harrisonburg, Virginia 22807
Email: jducey21@ufl.edu, duceyje@jmu.edu

Peter Sin
Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611–8105
Email: sin@ufl.edu

DOI: https://doi.org/10.1090/S0002-9939-2011-11462-X
Received by editor(s): February 28, 2011
Published electronically: December 21, 2011
Communicated by: Pham Huu Tiep
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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