Asymptotic enumeration of non-crossing partitions on surfaces - LIRMM - Laboratoire d’Informatique, de Robotique et de Microélectronique de Montpellier
Journal Articles Discrete Mathematics Year : 2013

Asymptotic enumeration of non-crossing partitions on surfaces

Abstract

We generalize the notion of non-crossing partition on a disk to general surfaces with boundary. For this, we consider a surface Σ and introduce the number CΣ(n) of non-crossing partitions of a set of n points lying on the boundary of Σ. Our main result is an asymptotic estimate for CΣ(n). The proofs use bijective techniques arising from map enumeration, joint with the symbolic method and singularity analysis on generating functions. An outcome of our results is that the exponential growth of CΣ(n) is the same as the one of the n-th Catalan number, i.e., does not change when we move from the case where Σ is a disk to general surfaces with boundary.

Dates and versions

lirmm-00804780 , version 1 (26-03-2013)

Identifiers

Cite

Dimitrios M. Thilikos, Ignasi Sau, Juanjo Rué. Asymptotic enumeration of non-crossing partitions on surfaces. Discrete Mathematics, 2013, pp.635-649. ⟨10.1016/j.disc.2012.12.011⟩. ⟨lirmm-00804780⟩
147 View
0 Download

Altmetric

Share

More