Enumeration of Eulerian and unicursal planar maps
type: Item
instance of: scholarly article
title: Enumeration of Eulerian and unicursal planar maps
zbMATH Open document ID: 1051.05049
author: Valery A. Liskovets
author: Timothy R. S. Walsh
published in: Discrete Mathematics
publication date: 2004-08-06T00:00:00Z
review text: By a unicursal map the authors mean a 2-cell embedding in the sphere of a graph (loops and multiple edges allowed) that has exactly two vertices of odd degree. Let \(U'(n)\) denote the number of rooted unicursal maps with \(n\) edges and let \(U_i'(n)\) the number of rooted unicursal maps with \(n\) edges and \(i\) vertices of degree 1 (clearly \(i = 0\), \(1\) or \(2\)). Among several results, the authors prove: Theorem 1. \(U'(n)= 2^{n-2}{2n\choose n}\), \(n\geq 1\), and for \(n\geq 2\), \(U_0'(n)= 2^{n-2} {n-2\over n} {2n-2\choose n-1}\), \(U_1'(n)= 2^{n-1}{2n-2\choose n-1}\), and \(U_2'(n)= 2^{n-2}{2n- 2\choose n-1}\).
Mathematics Subject Classification ID: 05C30
Mathematics Subject Classification ID: 05C10
zbMATH DE Number: 2083697
zbMATH Keywords: rooted planar map
zbMATH Keywords: unrooted Eulerian map
zbMATH Keywords: sum-free formula
zbMATH Keywords: Lagrange inversion
zbMATH Keywords: bipartite
zbMATH Keywords: embedding
reviewed by: Jack E. Graver
MaRDI profile type: Publication
full work available at URL: j.disc.2003.09.015
OpenAlex ID: W2164323648
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DOI: 10.1016/J.DISC.2003.09.015
description: scientific article; zbMATH DE number 2083697