The Distribution of Crossings of Chords Joining Pairs of 2n Points on a Circle

DOI10.2307/2005477zbMath0319.05004OpenAlexW4242349375MaRDI QIDQ4081259

John Riordan

Publication date: 1975

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2005477

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Recurrences (11B37) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Related Items (39)

Trees, forests, and total positivity. I: \(q\)-trees and \(q\)-forests matrices ⋮ Positroid stratification of orthogonal Grassmannian and ABJM amplitudes ⋮ Some multivariate master polynomials for permutations, set partitions, and perfect matchings, and their continued fractions ⋮ A bijective proof of a Touchard-Riordan formula ⋮ Exact moments of the Sachdev-Ye-Kitaev model up to order \(1/N^2\) ⋮ The combinatorics of q-Hermite polynomials and the Askey-Wilson integral ⋮ Formation of a giant component in the intersection graph of a random chord diagram ⋮ On a uniformly random chord diagram and its intersection graph ⋮ Perfect matchings with crossings ⋮ Octabasic Laguerre polynomials and permutation statistics ⋮ Improved enumeration of simple topological graphs ⋮ Pfaffians and nonintersecting paths in graphs with cycles: Grassmann algebra methods ⋮ Analytic combinatorics of chord and hyperchord diagrams with \(k\) crossings ⋮ Non-P-recursiveness of numbers of matchings or linear chord diagrams with many crossings ⋮ Set partitions, tableaux, and subspace profiles of regular diagonal operators ⋮ The normal distribution is \(\boxplus\)-infinitely divisible ⋮ Rhyming schemes: crossings and coverings ⋮ High temperature expansion of double scaled SYK ⋮ The combinatorics of a tree-like functional equation for connected chord diagrams ⋮ Crossings, Motzkin paths and moments ⋮ Pattern avoidance in matchings and partitions ⋮ Proofs of two conjectures of Kenyon and Wilson on Dyck tilings ⋮ Splitting subspaces and a finite field interpretation of the Touchard-Riordan formula ⋮ Touchard-Riordan formulas, T-fractions, and Jacobi's triple product identity ⋮ Major index for 01-fillings of moon polyominoes ⋮ A bijection between partially directed paths in the symmetric wedge and matchings ⋮ Deux propriétés combinatoires des nombres de Schröder ⋮ Chords, trees and permutations ⋮ Enumeration formulas for generalized \(q\)-Euler numbers ⋮ The \((q, t)\)-Gaussian process ⋮ The permuted analogues of three Catalan sets ⋮ Circular planar electrical networks: posets and positivity ⋮ Perfect matchings with crossings ⋮ Chord diagrams, exact correlators in spin glasses and black hole bulk reconstruction ⋮ Linear $k$-Chord Diagrams ⋮ On a class of linked diagrams. I: Enumeration ⋮ Crossings and nestings of matchings and partitions ⋮ The analysis of simple list structures ⋮ Sachdev–Ye–Kitaev model with an extra diagonal perturbation: phase transition in the eigenvalue spectrum

This page was built for publication: The Distribution of Crossings of Chords Joining Pairs of 2n Points on a Circle