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Ribbon decomposition and twisted Hurwitz numbers
Yurii Burman1; Raphaël Fesler2
1 Higher School of Economics, Moscow, Russia, and Independent University of Moscow
2 Higher School of Economics, Moscow, Russia
Mathematics Research Reports, Volume 5 (2024), pp. 1-19.

Ribbon decomposition is a way to obtain a surface with boundary (compact, not necessarily oriented) from a collection of disks by joining them with narrow ribbons attached to segments of the boundary. Counting ribbon decompositions gives rise to a “twisted” version of the classical Hurwitz numbers (studied earlier by G. Chapuy and M. Dołęga [2] in a different context) and of the cut-and-join equation. We also provide an algebraic description of these numbers and an explicit formula for them in terms of zonal polynomials.

Received:
Revised:
Published online:
DOI: 10.5802/mrr.19
Classification: 57N05, 05C30
Keywords: surface with boundary, Hurwitz number, Jack polynomial
Yurii Burman 1; Raphaël Fesler 2

1 Higher School of Economics, Moscow, Russia, and Independent University of Moscow
2 Higher School of Economics, Moscow, Russia
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Yurii Burman; Raphaël Fesler. Ribbon decomposition and twisted Hurwitz numbers. Mathematics Research Reports, Volume 5 (2024), pp. 1-19. doi : 10.5802/mrr.19. https://mrr.centre-mersenne.org/articles/10.5802/mrr.19/

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