### An alternative definition of the notion valuation in the theory of near polygons.

Bart De Bruyn UGent (2009) 16(6). p.1-14
abstract
Valuations of dense near polygons were introduced in \cite{DB-Va:1}. A valuation of a dense near polygon $\mathcal{S}=(\mathcal{P},\mathcal{L},\mathrm{I})$ is a map $from the point-set$\mathcal{P}$of$\mathcal{S}$to the set$\N$of nonnegative integers satisfying very nice properties with respect to the set of convex subspaces of$\mathcal{S}$. In the present paper, we give an alternative definition of the notion valuation and prove that both definitions are equivalent. In the case of dual polar spaces and many other known dense near polygons, this alternative definition can be significantly simplified. Please use this url to cite or link to this publication: author organization year type journalArticle (original) publication status published subject keyword valuation, dense near polygon journal title Electronic Journal of Combinatorics Electron. J. Combin. volume 16 issue 6 pages 1 - 14 Web of Science type Article Web of Science id 000262909300004 JCR category MATHEMATICS JCR impact factor 0.605 (2009) JCR rank 138/251 (2009) JCR quartile 3 (2009) ISSN 1077-8926 language English UGent publication? yes classification A1 copyright statement I don't know the status of the copyright for this publication id 879114 handle http://hdl.handle.net/1854/LU-879114 date created 2010-02-24 14:20:22 date last changed 2010-03-05 09:24:04 @article{879114, abstract = {Valuations of dense near polygons were introduced in {\textbackslash}cite\{DB-Va:1\}. A valuation of a dense near polygon \${\textbackslash}mathcal\{S\}=({\textbackslash}mathcal\{P\},{\textbackslash}mathcal\{L\},{\textbackslash}mathrm\{I\})\$is a map \$ from the point-set \${\textbackslash}mathcal\{P\}\$ of \${\textbackslash}mathcal\{S\}\$ to the set \${\textbackslash}N\$ of nonnegative integers satisfying very nice properties with respect to the set of convex subspaces of \${\textbackslash}mathcal\{S\}\$. In the present paper, we give an alternative definition of the notion valuation and prove that both definitions are equivalent. In the case of dual polar spaces and many other known dense near polygons, this alternative definition can be significantly simplified.},
author       = {De Bruyn, Bart},
issn         = {1077-8926},
journal      = {Electronic Journal of Combinatorics},
keyword      = {valuation,dense near polygon},
language     = {eng},
number       = {6},
pages        = {1--14},
title        = {An alternative definition of the notion valuation in the theory of near polygons.},
volume       = {16},
year         = {2009},
}

Chicago
De Bruyn, Bart. 2009. “An Alternative Definition of the Notion Valuation in the Theory of Near Polygons.” Electronic Journal of Combinatorics 16 (6): 1–14.
APA
De Bruyn, B. (2009). An alternative definition of the notion valuation in the theory of near polygons. Electronic Journal of Combinatorics, 16(6), 1–14.
Vancouver
1.
De Bruyn B. An alternative definition of the notion valuation in the theory of near polygons. Electronic Journal of Combinatorics. 2009;16(6):1–14.
MLA
De Bruyn, Bart. “An Alternative Definition of the Notion Valuation in the Theory of Near Polygons.” Electronic Journal of Combinatorics 16.6 (2009): 1–14. Print.