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The dual Yoshiara construction gives new extended generalized quadrangles

S.G. Barwick, Matthew R. Brown
2004 European journal of combinatorics (Print)  
This article extends this result and shows that in general the dual of S(O) is a new Yoshiara family, thus giving new extended generalized quadrangles.  ...  In 1998 Yoshiara showed that such a family gives rise to an extended generalized quadrangle of order (q + 1, q − 1). He also constructed such a family S(O) from a hyperoval O in PG(2, q).  ...  Acknowledgement This work was supported by the Australian Research Council.  ... 
doi:10.1016/j.ejc.2003.09.007 fatcat:pl6e4pubujatzbmbsup2za5c2y

Page 7248 of Mathematical Reviews Vol. , Issue 2001J [page]

2001 Mathematical Reviews  
We present a new family ¥'(@) of extended generalized quadrangles of order (¢ + 1,q —1) constructed from the dual of the Yoshiara construction “(@) [op. cit.] and show that each such extended generalized  ...  Harald Léwe (Braunschweig) 51E Finite geometry and special incidence structures 2001j:51006 SIE12 Ng, Siaw-Lynn (4-LNDHB; Egham); Wild, Peter R. (4-LNDHB; Egham) A new family of extended generalized quadrangles  ... 

Page 4935 of Mathematical Reviews Vol. , Issue 2000g [page]

2000 Mathematical Reviews  
Higher-dimensional dual arcs, for instance, first defined in full generality in the paper under review, are implicit in a number of new and old constructions, even in a well-known model for the Mathieu  ...  Dina Smit-Ghinelli (I-ROME; Rome) 2000¢:51006 51E12 05B25 51E21 SIE24 Yoshiara, Satoshi (J-OSAKK3-DM; Kashiwara) Extended generalized quadrangles. Algebraic combinatorics (Japanese) (Kyoto, 1998).  ... 

Page 6140 of Mathematical Reviews Vol. , Issue 93k [page]

1993 Mathematical Reviews  
Much less is known for the case in which stars of points are nonclassical finite thick generalized quadrangles.  ...  The purpose of this paper is to extend our results and to illustrate our methods by giving a complete characterization of some minihypers and codes meeting the Griesmer bound that previously have not been  ... 

A New Family of Extended Generalized Quadrangles of Order (q+ 1,q− 1)

Siaw-Lynn Ng, Peter R. Wild
2000 European journal of combinatorics (Print)  
We present a new family Y (O) of extended generalized quadrangles of order (q + 1, q − 1) constructed from the dual of the Yoshiara construction S(O) [6] and show that each such extended generalized quadrangle  ...  In this paper we show that any dual of the family S of planes defined by Yoshiara [6] also satisfies the same conditions.  ...  regular hyperoval, the dual S (k) of the Yoshiara construction S(k) is a new family of q + 3 planes satisfying conditions ( †).  ... 
doi:10.1006/eujc.1999.0345 fatcat:ys4joqe6abavtdcrmpinvcs4v4

A census of extended generalized quadrangles of order (q−1,q+1) and (q+1,q−1)

Alberto Del Fra, Antonio Pasini
1999 Discrete Mathematics  
A census of extended generalized quadrangles of order (q − 1; q + 1) and (q + 1; q − 1) Abstract We survey the known extended generalized quadrangles with point-residues of order (q − 1; q + 1) and (q  ...  + 1; q − 1) and construct a new inÿnite family of order (q + 1; q − 1) (q odd).  ...  It is proved in [10] The extended generalized quadrangle 4 (O; O * ) is the 2-fold quotient of a simply connnected ag-transitive geometry, say , constructed by Yoshiara [31] as the amalgam of a suitable  ... 
doi:10.1016/s0012-365x(99)00072-2 fatcat:5ow4a6qwvbfcjbkcl3mupoltmm

Page 1833 of Mathematical Reviews Vol. , Issue 99c [page]

1991 Mathematical Reviews  
Ivanov [Aleksandr Anatol’evich Ivanov], Affine extended dual polar spaces (107-121); Norman L.  ...  Dedicata 69 (1998), no. 2, 207-221; MR 98m:51005], each antiregular generalized quadrangle gives rise to semi-biplanes.  ... 

Volume Contents

2004 European journal of combinatorics (Print)  
dual Yoshiara construction gives new extended generalized quadrangles . . . . . . . . 377 CHANG, G.J., TONG, L.  ...  Construction of new extremal unimodular lattices . . . 549 KATO, M. and SEKIGUCHI, J., Regular polyhedral groups and reflection groups of rank four . . . . . . . . . . . . . . 565 LING, S., A family of  ... 
doi:10.1016/s0195-6698(04)00156-8 fatcat:oaxmjjvb2nfs7emq4ufzk3xzau

Tight sets and m-ovoids of generalised quadrangles

John Bamberg, Maska Law, Tim Penttila
2009 Combinatorica  
As a byproduct the following result is obtained: if S is a flock generalized quadrangle of order (s 2 , s), with s odd, then the point-line dual of S is a translation generalized quadrangle if and only  ...  We give a unified construction and prove the following. Theorem 1. The k-grassmannian of the polar space associated to Sp 2n (F) has generating rank 2n k − 2n k−2 if F is a field with Char(F) = 2.  ... 
doi:10.1007/s00493-009-2179-x fatcat:3lv4kl6qafbfdemivsj73n6miq

Point regular groups of automorphisms of generalised quadrangles

John Bamberg, Michael Giudici
2011 Journal of combinatorial theory. Series A  
We also construct point regular groups of automorphisms of the generalised quadrangle of order (q-1,q+1) obtained by Payne derivation from the classical symplectic quadrangle W(3,q).  ...  We study the point regular groups of automorphisms of some of the known generalised quadrangles.  ...  Acknowledgments The authors would like to thank Frank De Clerck, Bill Kantor, Tim Penttila, Gordon Royle and Pablo Spiga for their comments on a preliminary draft, and the anonymous referees.  ... 
doi:10.1016/j.jcta.2010.11.004 fatcat:bhuyyke62nep5kisycjwph2wqa

Dimensional dual hyperovals in projective spaces and c·AG∗-geometries

Cécile Huybrechts
2002 Discrete Mathematics  
In our intrinsic study of the ÿrst subject, we construct a new family of examples and deÿne the notions of quotient and universality.  ...  For the second subject, we restrict the class c · AG * of circular extensions of dual a ne spaces under the two geometrical conditions (LL) and (T) by showing that, apart from some extreme cases, every  ...  Acknowledgements The author is grateful to P.J. Cameron, A. Pasini and J.A. Thas for helpful conversations.  ... 
doi:10.1016/s0012-365x(01)00399-5 fatcat:2ue5vxx7wrgrhgjpsp7wzymsaa

AS-configurations and skew-translation generalised quadrangles [article]

John Bamberg, S.P. Glasby, Eric Swartz
2014 arXiv   pre-print
In this paper we prove results in the theory of STGQ giving (i) new structural information for a group G admitting an AS-configuration, (ii) a classification of the STGQ of order (8,8), and (iii) a classification  ...  of the STGQ of order (q,q) for odd q (using work of Ghinelli and Yoshiara).  ...  The first author acknowledges the support of the Australian Research Council Future Fellowship FT120100036.  ... 
arXiv:1405.5063v2 fatcat:apwx3seexbhzlk7cq5ocuintju

Distance-regular Cayley graphs with small valency

Edwin R. van Dam, Mojtaba Jazaeri
2019 Ars Mathematica Contemporanea  
We show that the incidence graphs of the known generalized hexagons are not Cayley graphs, and neither are some other distance-regular graphs that come from small generalized quadrangles or hexagons.  ...  We determine the distance-regular Cayley graphs with valency at most 4, the Cayley graphs among the distance-regular graphs with known putative intersection arrays for valency 5, and the Cayley graphs  ...  We note that similarly there are precisely two generalized quadrangles of order (3, 3) , and these are dual to each other.  ... 
doi:10.26493/1855-3974.1964.297 fatcat:pu2ispk3drfhpfj6mr3ar4yhby

Distance-regular Cayley graphs with small valency [article]

Edwin R. van Dam, Mojtaba Jazaeri
2019 arXiv   pre-print
We show that the incidence graphs of the known generalized hexagons are not Cayley graphs, and neither are some other distance-regular graphs that come from small generalized quadrangles or hexagons.  ...  We determine the distance-regular Cayley graphs with valency at most 4, the Cayley graphs among the distance-regular graphs with known putative intersection arrays for valency 5, and the Cayley graphs  ...  We thank Sasha Gavrilyuk, who, in the final stages of writing this paper, at a conference in Plzeň, pointed us to [27] for what he called Higman's method applied to generalized polygons.  ... 
arXiv:1808.01428v2 fatcat:acxku3se6ndihgakxsrkdpazaq

SIMPLE GROUPS, PRODUCT ACTIONS, AND GENERALIZED QUADRANGLES

JOHN BAMBERG, TOMASZ POPIEL, CHERYL E. PRAEGER
2017 Nagoya mathematical journal  
The classification of flag-transitive generalized quadrangles is a long-standing open problem at the interface of finite geometry and permutation group theory.  ...  Working toward this aim, we are led to investigate generalized quadrangles that admit a collineation group $G$ preserving a Cartesian product decomposition of the set of points.  ...  Acknowledgements We thank Elisa Covato and Tim Burness for making available to us the results quoted in Section 6, and Luke Morgan for helpful discussions.  ... 
doi:10.1017/nmj.2017.35 fatcat:4uwdtqg73zf6jpva2gxg33wiuq
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