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

Bart De Bruyn UGent (2009) Electronic Journal of Combinatorics. 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.