Results 21 to 30 of about 2,886,103 (258)

An Alternative Definition of the Notion Valuation in the Theory of Near Polygons [PDF]

The Electronic Journal of Combinatorics, 2009
Valuations of dense near polygons were introduced in [9]. A valuation of a dense near polygon ${\cal S}=({\cal P},{\cal L},{\rm I})$ is a map $f$ from the point-set ${\cal P}$ of ${\cal S}$ to the set $\Bbb N$ of nonnegative integers satisfying very nice
B. Bruyn
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Combinatorial Construction of Some Near Polygons

Journal of Combinatorial Theory, Series A, 1997
A near \(2n\)-gon is a linear incidence system \((P,L)\) satisfying: (i) every line contains at least two points, (ii) the point graph of \((P,L)\) is connected with diameter \(n\), (iii) for each point line pair \((p,l)\), there is a unique point \(q\) on \(l\) nearest \(p\). Note that near 4-gon is the same thing as a generalized quadrangle.
B. Cooperstein, E. Shult
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The Regular Near Polygons of Order (s, 2) [PDF]

Journal of Algebraic Combinatorics, 2004
A near polygon is a partial linear space \({\mathcal S}=({\mathcal P},{\mathcal L})\) with the property that for every point \(p\in {\mathcal P}\) and for every line \(L\in {\mathcal L}\) there exists a unique point on \(L\) nearest to \(p\). Here distances \(d\) are measured in the collinearity graph \(\Gamma\). If \(n=\text{ diam}(\Gamma)\), then \({\
Akira Hiraki, J. Koolen
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The glueing of near polygons

Bulletin of the Belgian Mathematical Society - Simon Stevin, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
B. Bruyn
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Some Extensions and Embeddings of Near Polygons [PDF]

Journal of Algebraic Combinatorics, 1993
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
H. Cuypers, T. Meixner
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A Higman-Haemers Inequality for Thick Regular Near Polygons [PDF]

Journal of Algebraic Combinatorics, 2004
Let \(\Gamma\) be a generalized \(n\)-gon of order \((s, t)\) (i.e. on every line there are exactly \(s+1\) points and every point lies on \(t+1\) lines). W. Feit and D. G. Higman showed that, apart from the ordinary polygons, finite examples only exist for \(n = 3, 4, 6, 8\) or \(12\). If \(s>1\) and \(t>1\), then \(n = 12\) is not possible.
Akira Hiraki, J. Koolen
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Near polygons having a big sub near polygon isomorphic to $\mathbb G_n$

Bulletin of the Belgian Mathematical Society - Simon Stevin, 2004
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
B. Bruyn
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Compatible spreads of symmetry in near polygons [PDF]

Journal of Algebraic Combinatorics, 2006
The author develops his own studies of near polygons. A spread of symmetry of a near polygon is a set of lines partitioning the point set and satisfying a certain property (explicit definitions are available in Section 1). These special spreads of a near polygon give rise to new near polygons, called glued near polygons.
B. Bruyn
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On the Uniqueness of Near Polygons with Three Points on Every Line

European Journal of Combinatorics, 2002
The author presents a criterion to decide whether two near \(2d\)-gons (A) with three points per line, (B) such that every two non collinear points which are both collinear with at least one point are collinear with at least two points, and (C) containing a big geodesically closed sub-near \(2(d-1)\)-gon \({\mathcal H}\), are isomorphic (\({\mathcal H}\
B. Bruyn
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On the Finiteness of Near Polygons with 3 Points on Every Line [PDF]

Journal of Algebraic Combinatorics, 2003
The author deals with near \(2d\)-gons. A {near \(2d\)-gon} is a partial linear space \(\Gamma = ({\mathcal P}, {\mathcal L}, I)\) satisfying the following two conditions: (1) For every point \(p \in {\mathcal P}\) and every line \(l \in {\mathcal L}\) there exists a unique point on \(l\) with minimal distance to \(p\), where the distance is measured ...
B. Bruyn
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