Fitxers
Tipus de document
ArticleVersió
Versió acceptadaData de publicació
Tots els drets reservats
Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/190456
Alternating Catalan numbers and cover with triple ramification
Títol de la revista
Director/Tutor
ISSN de la revista
Títol del volum
Recurs relacionat
Resum
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 $C_n$.
Matèries (anglès)
Citació
Citació
FARKAS, Gavril, et al. Alternating Catalan numbers and cover with triple ramification. Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. 2021. Vol. XXII, num. 2, pags. 665-690. ISSN 0391-173X. [consulted: 23 of May of 2026]. Available at: https://hdl.handle.net/2445/190456