Counting planar Eulerian orientations. (June 2018)
- Record Type:
- Journal Article
- Title:
- Counting planar Eulerian orientations. (June 2018)
- Main Title:
- Counting planar Eulerian orientations
- Authors:
- Elvey-Price, Andrew
Guttmann, Anthony J. - Abstract:
- Abstract: Inspired by the paper of Bonichon et al. (2016), we give a system of functional equations which characterise the ordinary generating function, U ( x ), for the number of planar Eulerian orientations counted by edges. We also characterise the ogf A ( x ), for 4-valent planar Eulerian orientations counted by vertices in a similar way. The latter problem is equivalent to the 6-vertex problem on a random lattice, widely studied in mathematical physics. While unable to solve these functional equations, they immediately provide polynomial-time algorithms for computing the coefficients of the generating function. From these algorithms we have obtained 100 terms for U ( x ) and 90 terms for A ( x ) . Analysis of these series suggests that they both behave as c o n s t ⋅ ( 1 − μ x ) ∕ log ( 1 − μ x ), where we conjecture that μ = 4 π for Eulerian orientations counted by edges and μ = 4 3 π for 4-valent Eulerian orientations counted by vertices.
- Is Part Of:
- European journal of combinatorics. Volume 71(2018)
- Journal:
- European journal of combinatorics
- Issue:
- Volume 71(2018)
- Issue Display:
- Volume 71, Issue 2018 (2018)
- Year:
- 2018
- Volume:
- 71
- Issue:
- 2018
- Issue Sort Value:
- 2018-0071-2018-0000
- Page Start:
- 73
- Page End:
- 98
- Publication Date:
- 2018-06
- Subjects:
- Combinatorial analysis -- Periodicals
Analyse combinatoire -- Périodiques
Combinatorial analysis
Periodicals
Electronic journals
511.6 - Journal URLs:
- http://www.sciencedirect.com/science/journal/01956698 ↗
http://www.elsevier.com/journals ↗
http://www.idealibrary.com ↗
http://firstsearch.oclc.org ↗
http://firstsearch.oclc.org/journal=0195-6698;screen=info;ECOIP ↗ - DOI:
- 10.1016/j.ejc.2018.02.040 ↗
- Languages:
- English
- ISSNs:
- 0195-6698
- Deposit Type:
- Legaldeposit
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library DSC - 3829.728200
British Library DSC - BLDSS-3PM
British Library HMNTS - ELD Digital store - Ingest File:
- 11412.xml