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Smallest cyclically covering subspaces of Fqn, and lower bounds in Isbell's conjecture
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dc.contributor.author | Cameron, Peter J. | |
dc.contributor.author | Ellis, David | |
dc.contributor.author | Raynaud, William | |
dc.date.accessioned | 2020-06-19T23:34:44Z | |
dc.date.available | 2020-06-19T23:34:44Z | |
dc.date.issued | 2019-10 | |
dc.identifier | 259186041 | |
dc.identifier | 32d12483-f1a8-4112-9c9a-c7b3cac58d7c | |
dc.identifier | 85067391476 | |
dc.identifier | 000482519400015 | |
dc.identifier.citation | Cameron , P J , Ellis , D & Raynaud , W 2019 , ' Smallest cyclically covering subspaces of F q n , and lower bounds in Isbell's conjecture ' , European Journal of Combinatorics , vol. 81 , pp. 242-255 . https://doi.org/10.1016/j.ejc.2019.06.004 | en |
dc.identifier.issn | 0195-6698 | |
dc.identifier.other | ORCID: /0000-0003-3130-9505/work/58755500 | |
dc.identifier.uri | https://hdl.handle.net/10023/20110 | |
dc.description.abstract | For a prime power q and a positive integer n, we say a subspace U of Fqn is cyclically covering if the union of the cyclic shifts of U is equal to Fqn. We investigate the problem of determining the minimum possible dimension of a cyclically covering subspace of Fqn. (This is a natural generalisation of a problem posed in 1991 by the first author.) We prove several upper and lower bounds, and for each fixed q, we answer the question completely for infinitely many values of n (which take the form of certain geometric series). Our results imply lower bounds for a well-known conjecture of Isbell, and a generalisation theoreof, supplementing lower bounds due to Spiga. We also consider the analogous problem for general representations of groups. We use arguments from combinatorics, representation theory and finite field theory. | |
dc.format.extent | 337068 | |
dc.language.iso | eng | |
dc.relation.ispartof | European Journal of Combinatorics | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject.lcc | QA | en |
dc.title | Smallest cyclically covering subspaces of Fqn, and lower bounds in Isbell's conjecture | en |
dc.type | Journal article | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.contributor.institution | University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra | en |
dc.identifier.doi | https://doi.org/10.1016/j.ejc.2019.06.004 | |
dc.description.status | Peer reviewed | en |
dc.date.embargoedUntil | 2020-06-20 |
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