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Affine semipartial geometries and projections of quadrics

Matthew R. Brown, Frank De Clerck, Mario Delanote
<span title="">2003</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/z77xaqun7bcxjkh75wb7iseaty" style="color: black;">Journal of combinatorial theory. Series A</a> </i> &nbsp;
A model of a semipartial geometry fully embedded in AGð4; qÞ; q even, due to Hirschfeld and Thas, is the spgðq À 1; q 2 ; 2; 2qðq À 1ÞÞ constructed by projecting the quadric Q À ð5; qÞ from a point of  ...  Debroey and Thas introduced semipartial geometries and determined the full embeddings of semipartial geometries in AGðn; qÞ for n ¼ 2 and 3. For n43 there is no such classification.  ...  GOA 12050300, while the third author was a Research Fellow supported by the Flemish Institute for the Promotion of Scientific and Technological Research in Industry (IWT), Grant No. IWT/SB/971002.  ... 
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Point derivation of partial geometries

Mario Delanote
<span title="">2003</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/54t3hgai4fhhthc74mj7z7tapu" style="color: black;">European journal of combinatorics (Print)</a> </i> &nbsp;
We introduce a new construction method for semipartial geometries, called point derivation, which is a generalization of the known theory of constructing partial quadrangles from generalized quadrangles  ...  De Clerck, my friend and former Ph.D. supervisor. I sincerely appreciate his encouragement, his support, and his helpful remarks.  ...  Without these my research and in particular this paper would not have been possible.  ... 
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Page 5483 of Mathematical Reviews Vol. , Issue 2004g [page]

<span title="">2004</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
(B-GHNT-PM; Ghent); De Clerck, Frank (B-GHNT-PM; Ghent); Delanote, Mario (B-GHNT-PM; Ghent) Affine semipartial geometries and projections of quadrics. (English summary) J. Combin. Theory Ser.  ...  A model of semipartial geometry fully embedded in AG(4,q), g even, due to Hirschfeld and Thas, is the spg(q — 1,q7.2,2q(q —1)) constructed by projecting the elliptic quadric Q~(5,q) from a point of PG(  ... 
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Page 157 of Mathematical Reviews Vol. , Issue 85a [page]

<span title="">1985</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
New spreads of the elliptic quadrics of PG(2n+ 1, q) are described and thus new examples of semipartial geometries are obtained. Christiane Lefévre-Percsy (Brussels) Willems, M. L.  ...  Salzmann, and the embedding of lines and planes in P is the same as in the affine space.  ... 
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Affine embeddings of (0,α)-geometries

F. De Clerck, N. De Feyter, J.A. Thas
<span title="">2006</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/54t3hgai4fhhthc74mj7z7tapu" style="color: black;">European journal of combinatorics (Print)</a> </i> &nbsp;
It is the purpose of this research note to give an overview of the recent results on full embeddings of (0, α)-geometries in affine spaces.  ...  A semipartial geometry which is not a partial geometry is called a proper semipartial geometry.  ...  Put U ∞ = U ∩ Π ∞ and let K ∞ be the set of points of U ∞ fixed by ϕ. Then K ∞ is the point set of a projective geometry PG(n − 2, 2) ⊆ U ∞ .  ... 
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Page 4016 of Mathematical Reviews Vol. , Issue 99f [page]

<span title="">1999</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
99f:51008 99f:51008 51E12 51D20 SIE14 Brown, Matthew R. (5-ADLD; Adelaide) Semipartial geometries and generalized quadrangles of order (,, r*), (English summary) Finite geometry and combinatorics (Deinze  ...  From the introduction: “Projective planes, affine planes, nets and their related structures (transversal designs, MOLS) have received a great deal of attention.  ... 
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The embedding of (0, 2)-geometries and semipartial geometries in AG(n, q)

Nikias De Feyter
<span title="2005-01-20">2005</span> <i title="Walter de Gruyter GmbH"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ryvwpqomgfbjpnwgp6a6o5jsr4" style="color: black;">Advances in Geometry</a> </i> &nbsp;
As a corollary we classify the semipartial geometries with α > 1 fully embedded in AG(n, q), but not as a linear representation.  ...  A (0, α)-geometry, α ≥ 3, fully embedded in AG(n, q) is always a linear representation [2]. In [3] the (0, 2)-geometries fully embedded in AG(3, q) are classified up to linear representations.  ...  De Clerck and J. A. Thas for their many helpful remarks and suggestions and for reading this paper. The embedding of (0, 2)-geometries in AG(n, q)  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1515/advg.2005.5.2.279">doi:10.1515/advg.2005.5.2.279</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hrshax2vgbam5fvq3ms73zhh3u">fatcat:hrshax2vgbam5fvq3ms73zhh3u</a> </span>
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Volume Contents

<span title="">2003</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/z77xaqun7bcxjkh75wb7iseaty" style="color: black;">Journal of combinatorial theory. Series A</a> </i> &nbsp;
Affine semipartial geometries and projections of quadrics . . . . . . . . . . 281 Zhi-Wei Sun. On Snevily's conjecture and restricted sumsets . . . . . . . 291 David S.  ...  Axiom of choice and chromatic number of the plane . . . . . . . . . . . . . . . . . . . . . . . 387 Jeremy Lovejoy.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0097-3165(03)00131-6">doi:10.1016/s0097-3165(03)00131-6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hmlhhudrrjek7n6wl6zzhaext4">fatcat:hmlhhudrrjek7n6wl6zzhaext4</a> </span>
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Page 3795 of Mathematical Reviews Vol. , Issue 91G [page]

<span title="">1991</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
She proves that every geometry in that class is a quotient of an affine hyperbolic quadric over a group of automorphisms of the quadric fixing all points at infinity of the affine space in which the quadric  ...  Rees consid- 51F Metric geometry 91g:51013 ered the class of Tits geometries of type C; in which every line is incident with precisely two planes, and showed that those geome- tries are either (projective  ... 
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Page 8746 of Mathematical Reviews Vol. , Issue 2000m [page]

<span title="">2000</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Mavron and Vladimir D. Tonchev, On symmetric nets and generalized Hadamard matrices from affine designs (180-187); Klaus Metsch, On blocking sets of quadrics (188-207); Alan R.  ...  Thas and Hendrik Van Maldeghem, Some remarks on embed- dings of the flag geometries of projective planes in finite projective spaces (217-222); Tran van Trung [Tran Van Trung], Construction of 3-designs  ... 
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Finite geometries

A. Blokhuis, J. W. P. Hirschfeld, D. Jungnickel, J. A. Thas
<span title="2008-02-15">2008</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/c45m6ttnaje4xbjsq7m2c6df2a" style="color: black;">Designs, Codes and Cryptography</a> </i> &nbsp;
De Clerck, Recent results on projective and affine full embeddings of (α, β)-geometries G.L. Ebert, Binary codes of odd order Buekenhout-Metz unitals Y.  ...  Metsch, Large caps of the Klein quadric 2 A. Pott, Cyclotomy, geometry, and perfect sequences B. Schmidt, Asymptotic nonexistence of dihedral difference sets L.  ...  Recent results on projective and affine full embeddings of (α, β)-geometries F.  ... 
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Page 363 of Mathematical Reviews Vol. , Issue 2002A [page]

<span title="">2002</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
51E14 05B25 05E30 Delanote, Mario (B-GHNT-PM; Ghent A new semipartial geometry.  ...  We prove that for m odd and under the condition of existence of an orthogonal spread, the graph INQ(2mm, 3 3 is the point graph of a new semipartial geometry SPQ(2m, 3 For the entire collection see MR  ... 
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The isomorphism problem for linear representations and their graphs [article]

Philippe Cara and Sara Rottey and Geertrui Van de Voorde
<span title="2013-01-10">2013</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
A linear representation Tn*(K) of a point set K is a point-line geometry, embedded in a projective space PG(n+1,q), where K is contained in a hyperplane.  ...  We put constraints on K which ensure that every automorphism of Tn*(K) is induced by a collineation of the ambient projective space.  ...  Introduction A natural question in finite geometry is the following. (Q) Let G 1 and G 2 be two geometries embedded in a projective space.  ... 
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Page 6130 of Mathematical Reviews Vol. , Issue 2003h [page]

<span title="">2003</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Summary: “The incidence structures known as (a, /)-geometries are a generalization of partial geometries and semipartial geome- tries.  ...  and affine planes.  ... 
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The embedding in AG(3,q) of (0,2)-geometries with no planar nets

Nikias De Feyter
<span title="">2005</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/z77xaqun7bcxjkh75wb7iseaty" style="color: black;">Journal of combinatorial theory. Series A</a> </i> &nbsp;
This paper is part of the classification of (0, )-geometries ( > 1) embedded in AG(n, q). We study (0, 2)-geometries of order (2 h − 1, t) embedded in AG(3, 2 h ) such that there are no planar nets.  ...  Acknowledgements The author acknowledges the support of a "Bijzonder Onderzoeksfonds" (BOF) grant at Ghent University. The author also thanks F. De Clerck and J.A.  ...  Thas for their helpful remarks and suggestions and for reading this text.  ... 
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