Abstract
In this paper we study the enumeration of diagrams of n chords joining 2n points on a circle in disjoint pairs. We establish limit laws for the following three parameters: number of components, size of the largest component, and number of crossings. We also find exact formulas for the moments of the distribution of number of components and number of crossings.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
P. Billingsley, Probability and measure, third edition, John Wiley and Sons (1995).
L. Comtet, Advanced Combinatorics, Reidel (1974).
N.G. De Bruijn, Asymptotic Methods in Analysis, Dover (1981).
P. Flajolet, Combinatorial aspects of continued fractions, Discrete Math. 32 (1980), 125 - 161.
P. Flajolet, J. Françon and J. Vuillemin, Sequence of operations analysis for dynamic data structures, J. Algorithms 1 (1980), 111 - 141.
P. Flajolet and M. Noy, Analytic Combinatorics of Non-crossing Configurations, Discrete Mathematics 204 (1999), 203 - 229.
P. Flajolet, C. Puech and J. Vuillemin, The analysis of simple list structures, Inform. Sci. 38 (1986), 121 - 146.
P. Flajolet and B. Salvy, unpublished manuscript.
P. Flajolet and R. Sedgewick, Analytic Combinatorics, book in preparation (individual chapters are available as INRIA Research Reports 1888, 2026, 2376, 2956, 3162 ).
M.E.H. Ismail, D. Stanton and G. Viennot, The combinatorics of q-Hermite polynomials and the Askey-Wilson integral, European J. Combin. 8 (1987), 379 - 392.
A. Nijenhuis and H.S. Wilf, The Enumeration of Connected Graphs and Linked Diagrams, J. Combinatorial Theory A 27 (1979), 356 - 359.
J.-G. Penaud, Une preuve bijective d'une formule de Touchard-Riordan, Discrete Mathematics 139 (1995), 347 - 360.
R.C. Read, The chord intersection problem Annals of the New York Academy of Sciences 139 (1979), 444-454
J. Riordan, The Distribution of Crossings of Chords Joining Pairs of 2n points on a Circle, Math. of Computation 29 (1975), 215 - 222.
R. Sedgewick and P. Flajolet, An introduction to the analysis of algorithms,Addison-Wesley (1996)
P.R. Stein, On a Class of Linked Diagrams, I. Enumeration J. of Combinatorial Theory A 24 (1978), 357-366
P.R. Stein and C.J. Everett, On a Class of Linked Diagrams, II. Asymptotics Discrete Mathematics 21 (1978), 309-318
A. Stoimenow, Enumeration of chord diagrams and an upper bound for Vassiliev invariants, J. Knot Theory Ramifications 7 (1998),93-114.
J. Touchard, Sur un problème de configurations et sur les fractions continues, Canad. J. Math. 4 (1952), 2 - 25.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Flajolet, P., Noy, M. (2000). Analytic Combinatorics of Chord Diagrams. In: Krob, D., Mikhalev, A.A., Mikhalev, A.V. (eds) Formal Power Series and Algebraic Combinatorics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04166-6_17
Download citation
DOI: https://doi.org/10.1007/978-3-662-04166-6_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08662-5
Online ISBN: 978-3-662-04166-6
eBook Packages: Springer Book Archive