On minimal blocking sets of the generalized quadrangle $Q(4, q)$
The generalized quadrangle $Q(4,q)$ arising from the parabolic quadric in $PG(4,q)$ always has an ovoid. It is not known whether a minimal blocking set of size smaller than $q^2 + q$ (which is not an ovoid) exists in $Q(4,q)$, $q$ odd. We present results on smallest blocking sets in $Q(4,q)$, $q$ od...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2005-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/3466/pdf |
| _version_ | 1827324069589024768 |
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| author | Miroslava Cimráková Veerle Fack |
| author_facet | Miroslava Cimráková Veerle Fack |
| author_sort | Miroslava Cimráková |
| collection | DOAJ |
| description | The generalized quadrangle $Q(4,q)$ arising from the parabolic quadric in $PG(4,q)$ always has an ovoid. It is not known whether a minimal blocking set of size smaller than $q^2 + q$ (which is not an ovoid) exists in $Q(4,q)$, $q$ odd. We present results on smallest blocking sets in $Q(4,q)$, $q$ odd, obtained by a computer search. For $q = 5,7,9,11$ we found minimal blocking sets of size $q^2 + q - 2$ and we discuss their structure. By an exhaustive search we excluded the existence of a minimal blocking set of size $q^2 + 3$ in $Q(4,7)$. |
| first_indexed | 2024-04-25T02:02:54Z |
| format | Article |
| id | doaj.art-659610a5e49640d88b1c96a6c5836c2a |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:02:54Z |
| publishDate | 2005-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-659610a5e49640d88b1c96a6c5836c2a2024-03-07T14:41:16ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502005-01-01DMTCS Proceedings vol. AE,...Proceedings10.46298/dmtcs.34663466On minimal blocking sets of the generalized quadrangle $Q(4, q)$Miroslava Cimráková0Veerle Fack1Research Group on Combinatorial Algorithms and Algorithmic Graph TheoryResearch Group on Combinatorial Algorithms and Algorithmic Graph TheoryThe generalized quadrangle $Q(4,q)$ arising from the parabolic quadric in $PG(4,q)$ always has an ovoid. It is not known whether a minimal blocking set of size smaller than $q^2 + q$ (which is not an ovoid) exists in $Q(4,q)$, $q$ odd. We present results on smallest blocking sets in $Q(4,q)$, $q$ odd, obtained by a computer search. For $q = 5,7,9,11$ we found minimal blocking sets of size $q^2 + q - 2$ and we discuss their structure. By an exhaustive search we excluded the existence of a minimal blocking set of size $q^2 + 3$ in $Q(4,7)$.https://dmtcs.episciences.org/3466/pdfgeneralized quadrangleblocking setsearch algorithm[info.info-dm] computer science [cs]/discrete mathematics [cs.dm][math.math-co] mathematics [math]/combinatorics [math.co] |
| spellingShingle | Miroslava Cimráková Veerle Fack On minimal blocking sets of the generalized quadrangle $Q(4, q)$ Discrete Mathematics & Theoretical Computer Science generalized quadrangle blocking set search algorithm [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] |
| title | On minimal blocking sets of the generalized quadrangle $Q(4, q)$ |
| title_full | On minimal blocking sets of the generalized quadrangle $Q(4, q)$ |
| title_fullStr | On minimal blocking sets of the generalized quadrangle $Q(4, q)$ |
| title_full_unstemmed | On minimal blocking sets of the generalized quadrangle $Q(4, q)$ |
| title_short | On minimal blocking sets of the generalized quadrangle $Q(4, q)$ |
| title_sort | on minimal blocking sets of the generalized quadrangle q 4 q |
| topic | generalized quadrangle blocking set search algorithm [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] |
| url | https://dmtcs.episciences.org/3466/pdf |
| work_keys_str_mv | AT miroslavacimrakova onminimalblockingsetsofthegeneralizedquadrangleq4q AT veerlefack onminimalblockingsetsofthegeneralizedquadrangleq4q |