K-classes for matroids and equivariant localization
To every matroid, we associate a class in the K-theory of the Grassmannian. We study this class using the method of equivariant localization. In particular, we provide a geometric interpretation of the Tutte polynomial. We also extend results of the second author concerning the behavior of such clas...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2011-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/2915/pdf |
| _version_ | 1797270389588492288 |
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| author | Alex Fink David Speyer |
| author_facet | Alex Fink David Speyer |
| author_sort | Alex Fink |
| collection | DOAJ |
| description | To every matroid, we associate a class in the K-theory of the Grassmannian. We study this class using the method of equivariant localization. In particular, we provide a geometric interpretation of the Tutte polynomial. We also extend results of the second author concerning the behavior of such classes under direct sum, series and parallel connection and two-sum; these results were previously only established for realizable matroids, and their earlier proofs were more difficult. |
| first_indexed | 2024-04-25T02:03:30Z |
| format | Article |
| id | doaj.art-ef303b17bf45407381118a30033f43b2 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:03:30Z |
| publishDate | 2011-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-ef303b17bf45407381118a30033f43b22024-03-07T14:49:33ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502011-01-01DMTCS Proceedings vol. AO,...Proceedings10.46298/dmtcs.29152915K-classes for matroids and equivariant localizationAlex Fink0David Speyer1North Carolina State University [Raleigh]University of Michigan [Ann Arbor]To every matroid, we associate a class in the K-theory of the Grassmannian. We study this class using the method of equivariant localization. In particular, we provide a geometric interpretation of the Tutte polynomial. We also extend results of the second author concerning the behavior of such classes under direct sum, series and parallel connection and two-sum; these results were previously only established for realizable matroids, and their earlier proofs were more difficult.https://dmtcs.episciences.org/2915/pdfmatroidtutte polynomialk-theoryequivariant localizationgrassmannian[math.math-co] mathematics [math]/combinatorics [math.co][info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| spellingShingle | Alex Fink David Speyer K-classes for matroids and equivariant localization Discrete Mathematics & Theoretical Computer Science matroid tutte polynomial k-theory equivariant localization grassmannian [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| title | K-classes for matroids and equivariant localization |
| title_full | K-classes for matroids and equivariant localization |
| title_fullStr | K-classes for matroids and equivariant localization |
| title_full_unstemmed | K-classes for matroids and equivariant localization |
| title_short | K-classes for matroids and equivariant localization |
| title_sort | k classes for matroids and equivariant localization |
| topic | matroid tutte polynomial k-theory equivariant localization grassmannian [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| url | https://dmtcs.episciences.org/2915/pdf |
| work_keys_str_mv | AT alexfink kclassesformatroidsandequivariantlocalization AT davidspeyer kclassesformatroidsandequivariantlocalization |