Publications of Stanley E. Payne

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  1. A tensor product action on q-clan geometry with q = 2e, LINEAR ALGEBRA AND ITS APPLICATIONS, 226-228 (1995):115-137.

  2. The fundamental theorem of q-clan geometry, DESIGNS, CODES AND CRYPTOGRAPHY, 8 (1996): 181 - 202.

  3. Building a cyclic q-clan, in MOSTLY FINITE GEOMETRIES, (ed. N. L. Johnson), Marcel Dekker, 1997, pp. 365 - 378 (with T. Penttila and G.F. Royle.)

  4. The Subiaco Notebook 1997

  5. Collineations and characterizations of generalized quadrangles of order (q+1,q-1), Supplement ai Rendiconti del Circolo Matematica de Palermo, Serie II, 53(1998), 137 -- 166 (with M. A. Miller).

  6. On infinite K-clan geometry, JOURNAL OF GEOMETRY, 63(1998), 1 -- 16. (with L. Bader)

  7. A problem on generalized quadrangles, JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 73(1998), 197 -- 204.

  8. Covers of PG(3,q) and of finite generalized quadrangles , BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY, 5(1998), 1 -- 16. (with A. Blokhuis, C. M. O'Keefe, L. Storme and H. Wilbrink)

  9. Flock generalized quadrangles and related structures: an update. Proceedings of the Academy Contact Forum 20 October 2000, eds. F. De Clerck, L. Storme, J. A. Thas, H. Van Maldeghem, Universa Press, Belgium, (2001), 61 -- 98.

  10. Generalized quadrangles with a unique grid through every two intersecting lines. BULLETIN OF THE ICA 35(2002), 47 -- 52. (with Bart De Bruyn)

  11. The Ghinelli-Löwe construction of generalized quadrangles: an exposition, 2002, (Also available at: http://www.mat.uniroma1.it/~combinat/quaderni.)(with D. Ghinelli)

  12. The Ghinelli-Löwe construction of generalized quadrangles. EUROPEAN JOURNAL OF COMBINATORICS 24(2003), 511 -- 516. (with D. Ghinelli)

  13. Notes on Elation Generalized Quadrangles, EUROPEAN JOURNAL OF COMBINATORICS 24(2003), 969 -- 981 (with K. Thas).

  14. The cyclic q-clans with q = 2e, ADVANCES IN GEOMETRY (special issue in honor of Adriano Barlotti) (2003), 158 -- 185 (with W. Cherowitzo).

  15. Spreads of T2(0), $\alpha$-flocks and ovals, DESIGNS, CODES AND CRYPTOGRAPHY. 31(2004), 252--282 (with M. Brown, C.M. O'Keefe, T. Penttila and G. Royle).

  16. The Stabilizer of the Adelaide Oval, DISCRETE MATHEMATICS 294(2005), 161 -- 173, (with J. A. Thas).

  17. Foundations of Elation Generalized Quadrangles, EUROPEAN JOURNAL OF COMBINATORICS 27(2006), 51 -- 62 (with K. Thas).

In Press and In Preparation

  1. Some notes on generalized quadrangles of order s with a span of regular points, CONTRIBUTIONS TO ALGEBRA AND GEOMETRY, to appear (with B. De Bruyn).

  2. Finite Groups that Admit Kantor Families, FINITE GEOMETRIES, GROUPS, AND COMPUTATION (Eds. Hulpke, Liebler, Penttila and Seress; Proceedings of the conference "Finite Geometries, Groups, and Computation", September 4 -- 9, 2004, Pingree Park, Colorado, USA).

  3. The Ghinelli-Löwe construction of generalized quadrangles: an exposition, by D. Ghinelli and S. E. Payne, also available at: http://www.mat.uniroma1.it/~combinat/quaderni.
    An abbreviated version of this last paper has appeared in the EUROPEAN JOURNAL OF COMBINATORICS, 2003, see below.

Chronological Listing

'67-'70'71-'75'76-'80'81-'85 '86-'90'91-'95'96-'00'01- 
2006

Foundations of Elation Generalized Quadrangles, EUROPEAN JOURNAL OF COMBINATORICS 27: 51 -- 62 (with K. Thas).

2005

The Stabilizer of the Adelaide Oval, DISCRETE MATHEMATICS 294: 161 -- 173, (with J. A. Thas).

2004

Spreads of T2(0), $\alpha$-flocks and ovals, DESIGNS, CODES AND CRYPTOGRAPHY. 31: 252--282 (with M. Brown, C.M. O'Keefe, T. Penttila and G. Royle).

2003

The q-clan geometries with q = 2e, 210 pages, (with I. Cardinali)

The Ghinelli-Löwe construction of generalized quadrangles, EUROPEAN JOURNAL OF COMBINATORICS, 24/25: 511 -- 516. (with Dina Ghinelli)

2002

Generalized quadrangles with a unique grid through every two intersecting lines. BULLETIN OF THE ICA 35: 47 -- 52. (with Bart De Bruyn)

2001

Flock generalized quadrangles and related structures: an update. Proceedings of the Academy Contact Forum 20 October 2000, eds. F. De Clerck, L. Storme, J. A. Thas, H. Van Maldeghem, Universa Press, Belgium, 61 -- 98.

2000

  1. The Law-Penttila q-clan geometries, FINITE GEOMETRIES, EDS. A. BLOKHUIS, ET AL., KLUWER, 295 -- 303. (Proceedings of the Fourth Isle of Thorns conference on Finnite Geometries, 16 -- 21 July, 2000, Sussex.)

  2. Association Scheme: a two page entry in the Encyclopaedia of Mathematics, Supplement II, ed. M. Hazewinkel, Kluwer Academic Pub.

1998

  1. Collineations and characterizations of generalized quadrangles of order (q+1,q-1), Supplement ai Rendiconti del Circolo Matematica de Palermo, Serie II, 53, 137 -- 166 (with M. A. Miller).

  2. On infinite K-clan geometry, JOURNAL OF GEOMETRY, 63: 1 -- 16 (with L. Bader).

  3. A problem on generalized quadrangles, JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 73: 197 -- 204.

  4. Covers of PG(3,q) and of finite generalized quadrangles , BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY, 5: 1 -- 16. (with A. Blokhuis,C. M. O'Keefe, L. Storme and H. Wilbrink)

1997

  1. Flocks of Laguerre Planes and Associated Geometries, in MOSTLY FINITE GEOMETRIES, (ed. N. L. Johnson), Marcel Dekker, pp. 51 - 122 (with N. L. Johnson).

  2. Building a cyclic q-clan, in MOSTLY FINITE GEOMETRIES, (ed. N. L. Johnson), Marcel Dekker, pp. 365 -- 378 (with T. Penttila and G.F. Royle.)

  3. The Subiaco Notebook , 147 pages.

1996

  1. Generalized quadrangles, in the { CRC Handbook of Combinatorial Designs, eds. C. Colbourn and J. Dinitz, CRC Press, Inc., 364 - 369.

  2. The fundamental theorem of q-clan geometry, DESIGNS, CODES AND CRYPTOGRAPHY, 8: 181 - 202.

1995

  1. Isomorphisms between Subiaco q-clan geometries, BULL. BELGIAN MATH. SOC., SIMON STEVIN, 2:197 - 222 (with T. Penttila and I. Pinneri).

  2. A tensor product action on q-clan geometry with q = 2e, LINEAR ALGEBRA AND ITS APPLICATIONS, 226-228:115-137.

1994

  1. Collineations of the Subiaco generalized quadrangles, BULL. BELGIAN MATH. SOC., SIMON STEVIN, 1: 427 - 438.

  2. On q-clan geometry, q = 2e, BULL. BELGIAN MATH. SOC., SIMON STEVIN, 1: 301 - 328 (with L. Bader and G. Lunardon).

  3. Spreads and ovoids in finite generalized quadrangles, GEOMETRIAE DEDICATA , 52: 227 - 253 (with J. A. Thas).

1993

  1. Coherent configurations derived from quasiregular points in generalized quadangles, in FINITE GEOMETRY AND COMBINATORICS (eds F. De Clerck et al.), Cambridge University Press, 327 - 339.

  2. Reconstructing a generalized quadrangle from its distance two association scheme, JOURNAL OF ALGEBRAIC COMBINATORICS 2: 261 - 266 (with S. A. Hobart).

1992

  1. Desarguesian finite generalized quadrangles are classical or dual classical, Designs, Codes and Cryptography, 1: 299 - 305, (with H. van Maldeghem and J. A. Thas).

  2. Collineations of the generalized quadrangles associated with q-clans, COMBINATORICS '90: Recent Trends and Applications, Proceedings of the Conference on Combinatorics, Gaeta, Italy, 20 - 27 May, 1990; pp. 449 - 461.

  3. (0,n)-Sets in a generalized quadrangle, COMBINATORICS '90: Recent Trends and Applications, A. Barlotti et.al. (Editors), Elsevier, 1992, pp. 139-157 (with A. Del Fra and D. Ghinelli).

  4. Generalized quadrangles derived from groups and having s=t+2, Journal of Combinatorial Mathematics and Combinatorial Computing, 12: 65 - 76.

1991

  1. Half Moufang implies Moufang for finite generalized quadrangles, Inventiones Mathematicae, 105: 153 - 156, (with J. A. Thas and H. Van Maldeghem).

  2. Conical flocks, partial flocks, derivation and generalized quadrangles, Geometriae Dedicata, 38: 229 - 243, (with J. A. Thas).

  3. Generalized quadrangles, BLT-sets, and Fisher flocks, Congressus Numerantium, 84: 161 - 192, (with J. A. Thas).

1990

  1. FINITE GEOMETRIES, BUILDINGS AND RELATED TOPICS, (edited by W. M. Kantor, R. A. Liebler, S. E. Payne, and E. E. Shult), Oxford University Press, Oxford.

  2. A census of finite generalized quadrangles, pp. 29-36 in FINITE GEOMETRIES, BUILDINGS AND RELATED TOPICS, Oxford University Press, Oxford.

  3. The generalized quadrangle with (s,t) = (3,5), Congressus Numerantium 77: 5 - 29.

  4. Tight pointsets in finite generalized quadrangles II, Congressus Numerantium, 77: 31 - 41.

  5. Local group actions on generalized quadrangles, Simon Stevin, 64: 249 - 284 (with L. A. Rogers).

1989

An essay on skew translation generalized quadrangles, Geometriae Dedicata, 32:93-118.

1988

  1. The Thas-Fisher generalized quadrangles, Annals of Discrete Math. (ed. M. Mari) 37:357-366.

  2. q-clans and generalized quadrangles, Quaderni Seminario Geometrie Combinatorie, Dipart. Matematica, Universita di Roma "La Sapienza," no. 79, Gennaio 1988.

  3. Le Ovali di Cherowitzo, Quaderni Seminario Geometrie Combinatorie, Dipart. Matematica, Universita di Roma "La Sapienza," no. 78, Gennaio 1988.

  4. Tight sets in quadrangoli generalizzati finiti, Quaderni Seminario Geometrie Combinatorie, Dipart. Matematica, Universita di Roma "La Sapienza," no. 80, Gennaio 1988.

  5. A family of ovals with few collineations, European Jour. of Combinatorics (with J.A. Thas and H. Gevaert), 9:353-362.

  6. Spreads, flocks and generalized quadrangles, Jour. of Geometry, 33:113-128.

1987

Tight pointsets in finite generalized quadrangles, Congressus Numerantium 60:243-260.

1986

  1. A survey of Aztec numbers and their uses, Chapter 8 in Native American Mathematics (ed. M.P. Closs), University of Texas PRess, 213-235 (with M.P. Closs).

  2. Hyperovals yield many GQ, Simon Stevin 60:211-225.

1985

  1. Hyperovals and generalized quadrangles, in Finite Geometries (eds. C.A. Baker & L.M. Batten), Marcel-Dekker, Inc., New York, 251-270.

  2. A garden of generalized quadrangles, Algebras, Groups and Geometries 3:323-354.

  3. A new infinite family of generalized quadrangles, Congressus Numerantium 49:115-128.

1984

Finite generalized quadrangles, Research Notes in Mathematics #110, Pitman Pub. Inc., London, 312 pp., (with J.A. Thas).

1983

  1. On the structure of translation generalized quadrangles, in Combinatorics 81 (eds. A. Barlotti, P.V. Ceccherini, G. Tallini), Annals of Discrete Mathematics, North-Holland Pub. Co., 661-665.

  2. Collineations of finite generalized quadrangles, in Finite Geometries: Proc. Conf. in Honor T.G. Ostrom, Vol. 82, Lecture Notes in Pure and Applied Math., Marcel Dekker, Inc. 361-390.

  3. Moufang conditions for finite generalized quadrangles, in Combinatorics 81 (eds. A. Barlotti, P.V. Ceccherini, G. Tallini), Annals of Discrete Mathematics, North-Holland Pub. Co., 745-752, (with J.A. Thas).

1982

  1. Payne, S.E., A family of skew translation generalized quadrangles of even order, Congressus Numerantium 36, Proc. 13th S.E. Conf. Combinatorics, Graph Theory and Comp., 127-135, (with C. Maneri).

  2. Arthropod encounter rate: a null model based on random motion, The American Naturalist, 119: 499-510, (with J. DeVita, D. Kelly).

1981

  1. Span-symmetric generalized quadrangles, in The Geometric Vein (eds. C. Davis, B. Grunbaum, F.A. Sherk), Spring-Verlag, 231-242.

  2. Generalized quadrangles and the Higman-Sims Technique, European J. Comb. 2, 79-89, (with J.A. Thas).

1980

  1. Generalized quadrangles as group coset geometries, Congressus Numerantium XXIX, Proc. S.E. Conf. Combinatorics, Graph Theory and Comp. 717-734.

  2. Moufang conditions for finite generalized quadrangles, in: Finite Geometries and Designs (eds. P.J. Cameron, J.W.P. Hirschfeld and D.R. Hughes) Cambridge`University Press, London Math. Soc. Lecture Notes Series 49, 275-303, (with J.A. Thas).

1979

Generalized Quadrangles as Amalgamations of Desarguesian Planes: The Multiplicative Case, Congressus Numerantium XXIV. Proc. 10th Conf. Combinatorics Graph Theory, and Comp. 787-794, (with R.B. Killgrove, and D.I. Kiel).

1978

  1. An unusual generalized quadrangle of order sixteen. Jour. Comb. Theory (A) 24: 50-74, (with James E. Conklin).

  2. Generalized quadrangles of order sixteen, Congressus Numerantium XII Proc. 9th S.E. Conf., Combinatorics, Graph Theory, and Comp. 555-565, (with R. Killgrove).

1977

  1. Generalized quadrangles of order 4, I and II, Journal of Combinatorial Theory, 22: 267-279, 280-288.

  2. Generalized quadrangles with symmetry II, Simon Stevin 50: 209-245.

1976

  1. Erratum to "Generalized relative difference sets," Proc. Amer. Math. Soc. 56: 392, (with C.W.H. Lam).

  2. Generalized quadrangles with symmetry, Simon Stevin 49: 3-32, 81-103, (with J.A. Thas).

  3. Translation generalized quadrangles of order eight, Congressus Numerantium XVII. Proc. 7th S.E. Conf. Comb. Graph Theory. Comp., 469-474.

  4. Polarities of generalized hexagons and perfect codes, Geometriae Dedicata 5: 525-528, (with P.J. Cameron, J.A. Thas).

  5. Classical finite generalized quadrangles: a combinatorial study, Ars Combinatoria 2: 57-110, (with J.A. Thas).

1975

  1. All generalized quadrangles of order 3 are known, Jour. Comb. Theory 18: 203-206.

  2. Skew translation generalized quadrangles, Congressus Numerantium XIV, Proc. 6th S.E. Conf. Comb. Graph Theory. Comp.: 485-504.

1974

  1. On maximizing det(A'A), Discrete Math. 10: 145-158.

  2. Generalized quadrangles of even order, Jour. Alg. 31: 367-391.

1973

  1. The construction of Hadamard matrices, Tech. Report ARL73-0117, Wright Patterson AFB, 88 pages.

  2. A restriction on the parameters of a subquadrangle, Bull. Amer. Math. Soc. 79: 747-748.

  3. Finite generalized quadrangles: a survey, Proceed. Int. Conf. Proj. Planes, Wash. State University Press, 219-261.

  4. A maximum determinant problem Tech Report ARL73-0195, Wright Patterson PFB, 25 pages.

1972

  1. Generalized quadrangles as amalgamations of projective planes, Jour. Alg. 22:102-136.

  2. Quadrangles of order (s-1, s+1), Jour. Alg. 22: 97-119.

  3. On the nonexistence of a class of configurations which are nearly generalized n-gons, Jour. Comb. Theory 12: 268-282.

  4. Nonisomorphic symmetric block designs derived from generalized quadrangles, Renc. Accad. Naz. Lincei LI: 893-902, (with M.M. Eich).

1971

  1. Nonisomorphic generalized quadrangles, Jour. Alg. 18: 201-212.

  2. The equivalence of certain generalized quadrangles, Jour. Comb. Theory 10: 284-289.

  3. Coset Geometries of some generalized semi-direct products of groups, The Ohio Jour. Sci. 17: 170-174.

  4. A geometric representation of certain generalized hexagons in PG(3,s), Jour. Comb. Theory 11: 181-191.

  5. Linear transformations of a finite field. Amer. Math. Monthly 78: 659-660.

  6. A complete determination of translation ovoids in finite desarguesian planes, Rend. Accad. Naz. Lincei LI: 226-229.

1970

  1. A nonexistence theorem for relative difference sets, Ill. Jour. Math. 14: 648-649.

  2. Generalized relative difference sets, Proc. Amer. Math. Soc. 25: 46-50.

  3. Affine representations of generalized quadrangles, Jour. Alg. 16: 473-485.

  4. Collineations of affinely represented generalized quadrangles, Jour. Alg. 16: 496-508.

1969

On v(1) × v(2)(n,s,t) Configurations, Jour. Comb. Theory 7: 1-14, (with M.F. Tinsley).

1968

  1. A Bruck-Ryser type nonexistence theorem, Bull. Amer. Math Soc. 74: 922.

  2. Symmetric representations of non-degenerate generalized n-gons, Proc. Amer. Math. Soc. 19: 1321-1326.

1967

A consequence of the non-existence of certain generalized polygons, Duke Math Jour. 34: 555-559.