Research Interests

my Publications/ Errata

my Seminar Slides

other Handouts

Open Problems

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G. Eric Moorhouse:

Publications/Errata

Comments/corrections on these publications are welcome by email ().

Ovoids and Lattices

  1. The non-existence of ovoids in O9(q), with Athula Gunawardena, Europ. J. Combinatorics 18 (1997), 171-173.
  2. Ovoids from the E8 root lattice, Geometriae Dedicata 46 (1993), 287-297.
  3. Root lattice constructions of ovoids, in Finite Geometry and Combinatorics, ed. F. De Clerck et. al., pp.269-275, Camb. Univ. Press, Cambridge (1993).
  4. Ovoids and translation planes from lattices, in Mostly Finite Geometries, ed. N. L. Johnson; Marcel Dekker Inc., 1997, pp.123-134.
  5. Fingerprints of r-ary ovoids in O+(8,p) and of their O+(6,p)-slices, technical report, 1999.
  6. The first thousand shells of the E8 root lattice, September, 2019

p-Ranks of Varieties

  1. Some p-ranks related to orthogonal spaces, with Aart Blokhuis, J. Algebraic Combinatorics 4 (1995), 295-316.
  2. Some p-ranks related to finite geometric structures, in Mostly Finite Geometries, ed. N. L. Johnson; Marcel Dekker Inc., 1997, pp.353-364.
  3. Some p-ranks related to Hermitian varieties, J. Stat. Plan. Inf. 56 (1996), 229-241.
  4. The p-rank of the Sp(4,p) Generalized Quadrangle, with Dom de Caen, preprint. This has subsequently been generalised by P. Sin to Sp(2m,p).
  5. Approaching Some Problems in Finite Geometry through Algebraic Geometry, pp.285-296 in Algorithmic Algebraic Combinatorics and Grobner Bases, ed. G. Jones, A. Jurišić, M. Muzychuk and I. Ponomarenko, Springer-Verlag, Berlin, 2009.

Algebraic Graph Theory

  1. A family of antipodal distance-regular graphs related to the classical Preparata codes, with D. de Caen and R. Mathon, J. Algebraic Combinatorics 4 (1995), 317-317.
  2. On the Chromatic Numbers of Planes, preprint.
  3. Double covers of symplectic dual polar graphs, with J. Williford, Discrete Math. 339 (2016) no.2, 571-588.
  4. The eigenvalues of the graphs D(4,q), with S. Sun and J. Williford, submitted to J. Combin. Theory B, 2016.

Two-Graphs

  1. Two-graphs and skew two-graphs in finite geometries, Linear Algebra and its Applications 226-228 (1995), 529-551.

Nets and Quasigroups

  1. Bruck nets, codes, and characters of loops, Designs, Codes and Cryptography 1 (1991), 7-29.
  2. Codes of Nets with Translations, in Advances in Finite Geometries and Designs, ed. J. Hirschfeld et. al.; Oxford Univ. Press, 1991, pp.327-336.
  3. On codes of Bruck nets and projective planes, in Coding Theory, Design Theory, Group Theory (Proceedings of the Marshall Hall Conference), ed. D. Jungnickel and S. A. Vanstone; J. Wiley & Sons, 1993, pp.237-242.
  4. Nets and Latin squares of small order, technical report, April 2001. (Under Construction)
  5. Bol loops of small order, technical report, June 2002. (Under Construction)
  6. Ranks of Nets, Quasigroups and Related Systems 14 (2006), 61-72.
  7. Codes of Nets and Projective Planes, pp. 207-216 in: Error-Correcting Codes, Finite Geometries and Cryptography, ed. Aiden A. Bruen and David L. Wehlau, Contemporary Mathematics 523, American Mathematical Society, Providence RI, 2010.
    For most purposes, this should replace the previously available manuscript Ranks of Nets and of Webs, very preliminary draft, 2005.

Generalized Hadamard Matrices

  1. The 2-Transitive Complex Hadamard Matrices, preprint, 32 pages.
  2. Uniqueness of sets of mutually unbiased bases of order 5, with Daniel P. May, 2009.

Projective Planes

  1. PSL(2,q) as a collineation group of projective planes of small order, Geometriae Dedicata 31 (1989), 63-88.
  2. PSL(3,q) and PSU(3,q) on planes of order q4, unpublished manuscript, 42 pages.
  3. Projective planes of small order, technical report, September 2000.
  4. Projective planes of order 25. All known planes of order 25 are listed, along with pertinent information including automorphism groups
  5. Projective planes of order 27. All known planes of order 27 are listed, along with pertinent information including automorphism groups
  6. Projective planes of order 49. All known planes of order 49 are listed, along with pertinent information including automorphism groups
  7. On projective planes of order less than 32, in Finite Geometries, Groups, and Computation, ed. A. Hulpke et. al.; de Gruyter, Berlin, 2006, pp.149-162.
  8. Embedding finite partial linear spaces in finite translation nets, with Jason Williford. Journal of Geometry 91 no.1-2 (2009), 73-83.
  9. Subplanes of order 3 in Hughes planes, with Cafer Caliskan, Electronic Journal of Combinatorics 18 (2011) no.1, Paper 2, 8 pp.
  10. Groups of projective planes with differing numbers of point and line orbits, with Tim Penttila, Journal of Algebra 399 (2014), 1013-1020.
    View 5-minute summary Summary of Orbits paper

Other Generalised Polygons

  1. Generalised polygons of small order, technical report, August 2003. (Under Construction)

Semibiplanes

  1. Reconstructing projective planes from semibiplanes, in Coding Theory and Design Theory, Part II: Design Theory, ed. D. Ray-Chaudhuri, Springer-Verlag, 1990, pp.280-285.
  2. On the construction of finite projective planes from homology semibiplanes, Europ. J. Combinatorics 11 (1990), 589-600.
  3. Planes, semibiplanes and related complexes, preprint, 6 pages.

Other

  1. A sufficient condition for an entire function to be a polynomial of degree one, with F. Jafari and J.-Cl. Evard, Nieuw Archief voor Wiskunde 12 (1994), 9-13.
  2. Partitioning the n-cube into sets with mutual distance 1, with A. Blokhuis, K. Metsch, R. Ahlswede, and S.L. Bezrukhov, Applied Math. Letters 6 (1993), 17-19.
  3. Partial spreads and flocks over infinite fields, Note di Matematica 29, Suppl. 1 (2009), 179-200.

Under Construction

/ revised January, 2017