Multispecies Weighted Hurwitz Numbers
The construction of hypergeometric 2D Toda τ-functions as generating functions for weighted Hurwitz numbers is extended to multispecies families. Both the enumerative geometrical significance of multispecies weighted Hurwitz numbers, as weighted enumerations of branched coverings of the Riemann sphe...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2015 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2015
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147164 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Multispecies Weighted Hurwitz Numbers / J. Harnad // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 30 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862554671589097472 |
|---|---|
| author | Harnad, J. |
| author_facet | Harnad, J. |
| citation_txt | Multispecies Weighted Hurwitz Numbers / J. Harnad // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 30 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The construction of hypergeometric 2D Toda τ-functions as generating functions for weighted Hurwitz numbers is extended to multispecies families. Both the enumerative geometrical significance of multispecies weighted Hurwitz numbers, as weighted enumerations of branched coverings of the Riemann sphere, and their combinatorial significance in terms of weighted paths in the Cayley graph of Sn are derived. The particular case of multispecies quantum weighted Hurwitz numbers is studied in detail.
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| first_indexed | 2025-11-25T22:08:57Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147164 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-25T22:08:57Z |
| publishDate | 2015 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Harnad, J. 2019-02-13T18:00:06Z 2019-02-13T18:00:06Z 2015 Multispecies Weighted Hurwitz Numbers / J. Harnad // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 30 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 05A15; 14H30; 33C70; 57M12 DOI:10.3842/SIGMA.2015.097 https://nasplib.isofts.kiev.ua/handle/123456789/147164 The construction of hypergeometric 2D Toda τ-functions as generating functions for weighted Hurwitz numbers is extended to multispecies families. Both the enumerative geometrical significance of multispecies weighted Hurwitz numbers, as weighted enumerations of branched coverings of the Riemann sphere, and their combinatorial significance in terms of weighted paths in the Cayley graph of Sn are derived. The particular case of multispecies quantum weighted Hurwitz numbers is studied in detail. This paper is a contribution to the Special Issue on Exact Solvability and Symmetry Avatars in honour of
 Luc Vinet. The full collection is available at http://www.emis.de/journals/SIGMA/ESSA2014.html.
 This work is an extension of a joint project [11, 12] with M. Guay-Paquet, in which the notion of
 infinite parametric families of weighted Hurwitz numbers was first introduced, combined with
 the notion of signed multispecies Hurwitz numbers as introduced in [15] with A.Yu. Orlov. The
 author would like to thank both these co-authors for helpful discussions. Work supported by
 the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Fonds de
 recherche du Qu´ebec – Nature et technologies (FRQNT). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Multispecies Weighted Hurwitz Numbers Article published earlier |
| spellingShingle | Multispecies Weighted Hurwitz Numbers Harnad, J. |
| title | Multispecies Weighted Hurwitz Numbers |
| title_full | Multispecies Weighted Hurwitz Numbers |
| title_fullStr | Multispecies Weighted Hurwitz Numbers |
| title_full_unstemmed | Multispecies Weighted Hurwitz Numbers |
| title_short | Multispecies Weighted Hurwitz Numbers |
| title_sort | multispecies weighted hurwitz numbers |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147164 |
| work_keys_str_mv | AT harnadj multispeciesweightedhurwitznumbers |