Quantum integer-valued polynomials
We define a q-deformation of the classical ring of integer-valued polynomials which we call the ring of quantum integer-valued polynomials. We show that this ring has a remarkable combinatorial structure and enjoys many positivity properties: For instance, the structure constants for this ring with...
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| Format: | Article |
| Language: | English |
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Springer US
2017
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| Online Access: | http://hdl.handle.net/1721.1/106857 https://orcid.org/0000-0002-1048-6644 https://orcid.org/0000-0002-0985-4788 |
| _version_ | 1826210433468465152 |
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| author | Harman, Nathan Reid Hopkins, Sam |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Harman, Nathan Reid Hopkins, Sam |
| author_sort | Harman, Nathan Reid |
| collection | MIT |
| description | We define a q-deformation of the classical ring of integer-valued polynomials which we call the ring of quantum integer-valued polynomials. We show that this ring has a remarkable combinatorial structure and enjoys many positivity properties: For instance, the structure constants for this ring with respect to its basis of q-binomial coefficient polynomials belong to N[q]. We then classify all maps from this ring into a field, extending a known classification in the classical case where q=1 . |
| first_indexed | 2024-09-23T14:49:50Z |
| format | Article |
| id | mit-1721.1/106857 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T14:49:50Z |
| publishDate | 2017 |
| publisher | Springer US |
| record_format | dspace |
| spelling | mit-1721.1/1068572022-10-01T22:46:41Z Quantum integer-valued polynomials Harman, Nathan Reid Hopkins, Sam Massachusetts Institute of Technology. Department of Mathematics Harman, Nathan Reid Hopkins, Sam We define a q-deformation of the classical ring of integer-valued polynomials which we call the ring of quantum integer-valued polynomials. We show that this ring has a remarkable combinatorial structure and enjoys many positivity properties: For instance, the structure constants for this ring with respect to its basis of q-binomial coefficient polynomials belong to N[q]. We then classify all maps from this ring into a field, extending a known classification in the classical case where q=1 . National Science Foundation (U.S.). Graduate Research Fellowship Program (Grant No. 1122374) 2017-02-03T21:15:53Z 2017-08-06T05:00:04Z 2016-10 2016-02 2017-02-01T04:41:17Z Article http://purl.org/eprint/type/JournalArticle 0925-9899 1572-9192 http://hdl.handle.net/1721.1/106857 Harman, Nate, and Sam Hopkins. “Quantum Integer-Valued Polynomials.” Journal of Algebraic Combinatorics 45, no. 2 (October 4, 2016): 601–628. https://orcid.org/0000-0002-1048-6644 https://orcid.org/0000-0002-0985-4788 en http://dx.doi.org/10.1007/s10801-016-0717-3 Journal of Algebraic Combinatorics Article 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. Springer Science+Business Media New York application/pdf Springer US Springer US |
| spellingShingle | Harman, Nathan Reid Hopkins, Sam Quantum integer-valued polynomials |
| title | Quantum integer-valued polynomials |
| title_full | Quantum integer-valued polynomials |
| title_fullStr | Quantum integer-valued polynomials |
| title_full_unstemmed | Quantum integer-valued polynomials |
| title_short | Quantum integer-valued polynomials |
| title_sort | quantum integer valued polynomials |
| url | http://hdl.handle.net/1721.1/106857 https://orcid.org/0000-0002-1048-6644 https://orcid.org/0000-0002-0985-4788 |
| work_keys_str_mv | AT harmannathanreid quantumintegervaluedpolynomials AT hopkinssam quantumintegervaluedpolynomials |