On $k$-simplexes in $(2k-1)$-dimensional vector spaces over finite fields
We show that if the cardinality of a subset of the $(2k-1)$-dimensional vector space over a finite field with $q$ elements is $\gg q^{2k-1-\frac{1}{ 2k}}$, then it contains a positive proportional of all $k$-simplexes up to congruence.
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2009-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
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| Online Access: | https://dmtcs.episciences.org/2701/pdf |
| _version_ | 1797270367868289024 |
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| author | Le Anh Vinh |
| author_facet | Le Anh Vinh |
| author_sort | Le Anh Vinh |
| collection | DOAJ |
| description | We show that if the cardinality of a subset of the $(2k-1)$-dimensional vector space over a finite field with $q$ elements is $\gg q^{2k-1-\frac{1}{ 2k}}$, then it contains a positive proportional of all $k$-simplexes up to congruence. |
| first_indexed | 2024-04-25T02:03:09Z |
| format | Article |
| id | doaj.art-9ee185b23db84c4bb7ca27260d4c0871 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:03:09Z |
| publishDate | 2009-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-9ee185b23db84c4bb7ca27260d4c08712024-03-07T14:45:40ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502009-01-01DMTCS Proceedings vol. AK,...Proceedings10.46298/dmtcs.27012701On $k$-simplexes in $(2k-1)$-dimensional vector spaces over finite fieldsLe Anh Vinh0Department of Mathematics [Cambridge]We show that if the cardinality of a subset of the $(2k-1)$-dimensional vector space over a finite field with $q$ elements is $\gg q^{2k-1-\frac{1}{ 2k}}$, then it contains a positive proportional of all $k$-simplexes up to congruence.https://dmtcs.episciences.org/2701/pdffinite non-euclidean graphsspectral graphsdistance problemfinite euclidean graphs[math.math-co] mathematics [math]/combinatorics [math.co][info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| spellingShingle | Le Anh Vinh On $k$-simplexes in $(2k-1)$-dimensional vector spaces over finite fields Discrete Mathematics & Theoretical Computer Science finite non-euclidean graphs spectral graphs distance problem finite euclidean graphs [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| title | On $k$-simplexes in $(2k-1)$-dimensional vector spaces over finite fields |
| title_full | On $k$-simplexes in $(2k-1)$-dimensional vector spaces over finite fields |
| title_fullStr | On $k$-simplexes in $(2k-1)$-dimensional vector spaces over finite fields |
| title_full_unstemmed | On $k$-simplexes in $(2k-1)$-dimensional vector spaces over finite fields |
| title_short | On $k$-simplexes in $(2k-1)$-dimensional vector spaces over finite fields |
| title_sort | on k simplexes in 2k 1 dimensional vector spaces over finite fields |
| topic | finite non-euclidean graphs spectral graphs distance problem finite euclidean graphs [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| url | https://dmtcs.episciences.org/2701/pdf |
| work_keys_str_mv | AT leanhvinh onksimplexesin2k1dimensionalvectorspacesoverfinitefields |