Corpus ID: 236493588

Surgery in dimension 1+1 and Hurwitz numbers

  title={Surgery in dimension 1+1 and Hurwitz numbers},
  author={Yurii Burman and R. Fesler},
Surgery in dimension 1+1 describes how to obtain a surface with boundary (compact, not necessarily oriented) from a collection of disks by joining them with narrow ribbons attached to the boundary. Counting the ways to do it gives rise to a “twisted” version of the classical Hurwitz numbers and of the cut-and-join equation. 

Figures from this paper


An algebro-geometric proof of Witten's conjecture
We present a new proof of Witten's conjecture. The proof is based on the analysis of the relationship between intersection indices on moduli spaces of complex curves and Hurwitz numbers enumeratingExpand
Brick tabloids and the connection matrices between bases of symmetric functions
A new set of combinatorial objects called λ-brick tabloids and its variants are introduced, which are used to give combinatorially interpretations of the entries for twelve of the transition matrices between natural bases of Hn. Expand
Cycle factorizations and 1-faced graph embeddings
Summing over all possible factorizations of n-cycles the authors obtain a polynomial that happens to admit a closed expression and deduce a formula for the number of 1-faced embeddings of a given graph. Expand
Tree-like Properties of Cycle Factorizations
It is shown that a certain class of transpositions of a factorization corresponds naturally under the authors' bijection to leaf edges (incident with a vertex of degree 1) of a tree, and a generalization of this fact is given. Expand
Symmetric functions and Hall polynomials
I. Symmetric functions II. Hall polynomials III. HallLittlewood symmetric functions IV. The characters of GLn over a finite field V. The Hecke ring of GLn over a finite field VI. Symmetric functionsExpand
Enumerative Combinatorics: Volume 1
Richard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition ofExpand
Augmented monomials in terms of power sums
  • M. Merca
  • Computer Science, Medicine
  • SpringerPlus
  • 2015
This paper develops a simple recursive formula for the expansion of the augmented monomial symmetry functions into power sum symmetric functions and presents two algorithms that can be used to expressing the augmentedmonomial symmetric function in terms of the power sum symmetry functions. Expand
Reflection Groups And Coxeter Groups
The reflection groups and coxeter groups is universally compatible with any devices to read and is available in the digital library an online access to it is set as public so you can download it instantly. Expand
By Corollary 3.9 twisted Schur polynomials s λ , λ ∈ Λ n , form a basis in C
    The mapping ξ : Λ → Z (where Λ is the set of partitions) is strictly monotonic