• Corpus ID: 119325700

Asymptotics of lieanders with fixed composition sizes

@article{Delecroix2018AsymptoticsOL,
  title={Asymptotics of lieanders with fixed composition sizes},
  author={Vincent Delecroix},
  journal={arXiv: Combinatorics},
  year={2018}
}
  • V. Delecroix
  • Published 10 December 2018
  • Mathematics
  • arXiv: Combinatorics
Lieanders are special cases of meanders and first appeared in connection with Lie algebras. Using the results from the author with E. Goujard, P. Zograf and A. Zorich, we prove a polynomial asymptotics for the number of lieanders with fixed composition sizes as the number of arches tend to infinity. The coefficients of the asymptotics are rational numbers divided by an even power of pi. 

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References

SHOWING 1-10 OF 19 REFERENCES
Meanders and the Temperley-Lieb algebra
The statistics of meanders is studied in connection with the Temperley-Lieb algebra. Each (multi-component) meander corresponds to a pair of reduced elements of the algebra. The assignment of a
Right-angled billiards and volumes of moduli spaces of quadratic differentials on $\mathbb{C}P^1$
We use the relation between the volumes of the strata of meromorphic quadratic differentials with at most simple poles on the Riemann sphere and counting functions of the number of (bands of) closed
Connected components of meanders: I. Bi-rainbow meanders
Closed meanders are planar configurations of one or several disjoint closed Jordan curves intersecting a given line or curve transversely. They arise as shooting curves of parabolic PDEs in one space
ENUMERATION OF MEANDERS AND MASUR–VEECH VOLUMES
A meander is a topological configuration of a line and a simple closed curve in the plane (or a pair of simple closed curves on the 2-sphere) intersecting transversally. Meanders can be traced back
Plane and Projective Meanders
Contribution of one-cylinder square-tiled surfaces to Masur-Veech volumes
We compute explicitly the absolute contribution of square-tiled surfaces having a single horizontal cylinder to the Masur-Veech volume of any ambient stratum of Abelian differentials. The resulting
Long cycles in abc-permutations
An abc-permutation is a permutation σabc∈Sn obtained by exchanging an initial block of length a and a final block of length c of {1,…,n}, where n=a+b+c. In this note we compute the limit of the
An Introduction to the Theory of Numbers
  • E. T.
  • Mathematics
    Nature
  • 1946
THIS book must be welcomed most warmly into X the select class of Oxford books on pure mathematics which have reached a second edition. It obviously appeals to a large class of mathematical readers.
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