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

(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:
http://hdl.handle.net/1854/LU-879114

- author
- Bart De Bruyn UGent
- organization
- year
- 2009
- 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.