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Multispecies Weighted Hurwitz Numbers
Репозиторій DSpace/Manakin
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- Фізико-технічні та математичні науки
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2015, том 11
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- Symmetry, Integrability and Geometry: Methods and Applications, 2015, том 11, випуск за цей рік
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Multispecies Weighted Hurwitz Numbers
Інший ID:
2010 Mathematics Subject Classification: 05A15; 14H30; 33C70; 57M12
DOI:10.3842/SIGMA.2015.097
DOI:10.3842/SIGMA.2015.097
Посилання:
Multispecies Weighted Hurwitz Numbers / J. Harnad // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 30 назв. — англ.
Підтримка:
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).
Дата:
2015
Переглядів:
584
Завантажень:
257
Анотація:
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.
