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RECURSIONS FOR CHARACTERISTIC NUMBERS OF GENUS ONE PLANE CURVES
CHARACTERISTIC PLANE CURVES
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2015/7/14
Characteristic numbers of families of maps of nodal curves to P2 are de ned as
intersection of natural divisor classes. (This de nition agrees with the usual de nition for
families of plane curves.)...
GENUS 0 AND 1 HURWITZ NUMBERS: RECURSIONS, FORMULAS, AND GRAPH-THEORETIC INTERPRETATIONS
RECURSIONS FORMULAS GRAPH-THEORETIC
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2015/7/14
We derive a closed-form expression for all genus 1 Hurwitz numbers, and give a
simple new graph-theoretic interpretation of Hurwitz numbers in genus 0 and 1. (Hurwitz
numbers essentially count irred...
Recursions in Calogero-Sutherland Model Based on Virasoro Singular Vectors
Calogero-Sutherland Model Jack Symmetric Function Recursion Relations Integral Representation
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2011/10/9
Abstract: The present work is much motivated by finding an explicit way in the construction of the Jack symmetric function, which is the spectrum generating function for the Calogero-Sutherland(CS) mo...
Sums of Ceiling Functions Solve Nested Recursions
Nested recursion Ceiling function Formal satisfaction Equivalence class
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2011/9/15
Abstract: It is known that, for given integers s \geq 0 and j > 0, the nested recursion R(n) = R(n - s - R(n - j)) + R(n - 2j - s - R(n - 3j)) has a closed form solution for which a combinatorial inte...
The SL_3 Jones polynomial of the trefoil: a case study of $q$-holonomic recursions
The SL_3 Jones polynomial $q$-holonomic recursions
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2010/12/27
The SL_3 colored Jones polynomial of the trefoil knot is a $q$-holonomic sequence of two variables with natural origin, namely quantum topology. The paper presents an explicit set of generators for th...
Asymptotics of stationary solutions of multivariate stochastic recursions with heavy tailed inputs and related limit theorems
stationary solutions multivariate stochastic recursions related limit theorems
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2010/11/12
Let $\Phi_n$ be an i.i.d. sequence of Lipschitz mappings of $\R^d$. We study the Markov chain $\{X_n^x\}_{n=0}^\8$ on $\R^d$ defined by the recursion $X_n^x = \Phi_n(X^x_{n-1})$, $n\ge 0$, $X_0=x\in\...
A generalized backwards scheme for solving non monotonic stochastic recursions
Stochastic recursions Stationary solutions Enriched probability space
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2010/12/1
We propose an explicit construction of a stationary solution for a stochastic recursion of the form X ◦q = j(X) on a partially-ordered Polish space, when the monotonicity of j is not assumed. Un...