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dc.contributor.authorClark, Pete L.
dc.contributor.authorForrow, Aden
dc.contributor.authorSchmitt, John R.
dc.date.accessioned2017-02-02T21:59:54Z
dc.date.available2017-03-01T16:14:47Z
dc.date.issued2016-05
dc.date.submitted2014-05
dc.identifier.issn0209-9683
dc.identifier.issn1439-6912
dc.identifier.urihttp://hdl.handle.net/1721.1/106843
dc.description.abstractWe present a restricted variable generalization of Warning’s Second Theorem (a result giving a lower bound on the number of solutions of a low degree polynomial system over a finite field, assuming one solution exists). This is analogous to Schauz-Brink’s restricted variable generalization of Chevalley’s Theorem (a result giving conditions for a low degree polynomial system not to have exactly one solution). Just as Warning’s Second Theorem implies Chevalley’s Theorem, our result implies Schauz-Brink’s Theorem. We include several combinatorial applications, enough to show that we have a general tool for obtaining quantitative refinements of combinatorial existence theorems. Let q = p[superscript ℓ] be a power of a prime number p, and let F[subscript q] be “the” finite field of order q. For a[subscript 1],...,a[subscript n], N∈Z[superscript +], we denote by m(a[subscript 1],...,a[subscript n];N)∈Z[superscript +] a certain combinatorial quantity defined and computed in Section 2.1.en_US
dc.publisherSpringer Berlin Heidelbergen_US
dc.relation.isversionofhttp://dx.doi.org/10.1007/s00493-015-3267-8en_US
dc.rightsArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.en_US
dc.sourceSpringer Berlin Heidelbergen_US
dc.titleWarning’s Second Theorem with restricted variablesen_US
dc.typeArticleen_US
dc.identifier.citationClark, Pete L., Aden Forrow, and John R. Schmitt. “Warning’s Second Theorem with Restricted Variables.” Combinatorica (2016): n. pag.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematicsen_US
dc.contributor.mitauthorForrow, Aden
dc.relation.journalCombinatoricaen_US
dc.eprint.versionAuthor's final manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dc.date.updated2017-02-02T15:20:25Z
dc.language.rfc3066en
dc.rights.holderJános Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg
dspace.orderedauthorsClark, Pete L.; Forrow, Aden; Schmitt, John R.en_US
dspace.embargo.termsNen
dc.identifier.orcidhttps://orcid.org/0000-0001-8316-5369
mit.licensePUBLISHER_POLICYen_US
mit.metadata.statusComplete


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