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DC Field | Value | Language |
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dc.contributor.author | Farkas, Gavril | - |
dc.contributor.author | Moschetti, Riccardo | - |
dc.contributor.author | Naranjo del Val, Juan Carlos | - |
dc.contributor.author | Pirola, Gian Pietro | - |
dc.date.accessioned | 2022-11-04T10:38:01Z | - |
dc.date.available | 2022-11-04T10:38:01Z | - |
dc.date.issued | 2021-06-24 | - |
dc.identifier.issn | 0391-173X | - |
dc.identifier.uri | http://hdl.handle.net/2445/190456 | - |
dc.description.abstract | The Catalan numbers $C_n:=\frac{1}{n+1}\left(\begin{array}{c}2 n \\ n\end{array}\right)$ form one of the most ubiquitous sequence in classical combinatorics. Stanley's book [St] lists 66 different manifestations of these numbers in various counting problems. In the theory of algebraic curves, the Catalan number $C_n$ counts the covers $C \rightarrow \mathbb{P}^1$ of minimal degree $n+1$ from a general curve $C$ of genus $2 n$. Each such cover has simple ramification and its monodromy group equals $S_{n+1}$. By degenerating $C$ to a rational $g$-nodal curve, it was already known to Castelnuovo $[\mathrm{C}]$ that the number of such covers coincides with the degree of the Grassmannian $G(2, n+2)$ in its Plücker embedding, which is well-known to equal $C_n$. | - |
dc.format.extent | 26 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | - |
dc.publisher | Centro Edizioni Scuola Normale Superiore di Pisa | - |
dc.relation.isformatof | Versió postprint del document publicat a: https://doi.org/10.2422/2036-2145.201909_009 | - |
dc.relation.ispartof | Annali della Scuola Normale Superiore di Pisa. Classe di Scienze, 2021, vol. XXII, num. 2, p. 665-690 | - |
dc.relation.uri | https://doi.org/10.2422/2036-2145.201909_009 | - |
dc.rights | (c) Centro Edizioni Scuola Normale Superiore di Pisa, 2021 | - |
dc.source | Articles publicats en revistes (Matemàtiques i Informàtica) | - |
dc.subject.classification | Corbes algebraiques | - |
dc.subject.classification | Geometria algebraica | - |
dc.subject.classification | Teoria de grups | - |
dc.subject.classification | Combinatòria (Matemàtica) | - |
dc.subject.other | Algebraic curves | - |
dc.subject.other | Algebraic geometry | - |
dc.subject.other | Group theory | - |
dc.subject.other | Combinations | - |
dc.title | Alternating Catalan numbers and cover with triple ramification | - |
dc.type | info:eu-repo/semantics/article | - |
dc.type | info:eu-repo/semantics/acceptedVersion | - |
dc.identifier.idgrec | 695126 | - |
dc.date.updated | 2022-11-04T10:38:01Z | - |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | - |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
Files in This Item:
File | Description | Size | Format | |
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695126.pdf | 257.38 kB | Adobe PDF | View/Open |
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