منابع مشابه
Increasing trees and Kontsevich cycles
It is known that the combinatorial classes in the cohomology of the mapping class group of punctures surfaces defined by Witten and Kontsevich are polynomials in the adjusted Miller–Morita–Mumford classes. The leading coefficient was computed in [4]. The next coefficient was computed in [6]. The present paper gives a recursive formula for all of the coefficients. The main combinatorial tool is ...
متن کاملGraph Cohomology and Kontsevich Cycles
We use the duality between compactly supported cohomology of the associative graph complex and the cohomology of the mapping class group to show that the duals of the Kontsevich cycles [Wλ] correspond to polynomials in the Miller-Morita-Mumford classes. We also compute the coefficients of the first two terms of this polynomial. This extends the results of [Igu], giving a more detailed answer to...
متن کاملSpanning Trees and a Conjecture of Kontsevich
Kontsevich conjectured that the number of zeros over the field Fq of a certain polynomial QG associated with the spanning trees of a graph G is a polynomial function of q. We show the connection between this conjecture, the Matrix-Tree Theorem, and orthogonal geometry. We verify the conjecture in certain cases, such as the complete graph, and discuss some modifications and extensions.
متن کاملOn Rainbow Trees and Cycles
We derive sufficient conditions for the existence of rainbow cycles of all lengths in edge colourings of complete graphs. We also consider rainbow colorings of a certain class of trees.
متن کاملIncreasing trees and alternating permutations
In this article we consider some increasing trees, the number of which is equal to the number of alternating (updown) permutations, that is, permutations of the form σ(1) < σ(2) > σ(3) < ... . It turns out that there are several such classes of increasing trees, each of which is interesting in itself. Special attention is paid to the study of various statistics on these trees, connected with th...
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ژورنال
عنوان ژورنال: Geometry & Topology
سال: 2004
ISSN: 1364-0380,1465-3060
DOI: 10.2140/gt.2004.8.969