Planar rooted trees and Baker-Campbell-Hausdorff formula

Today on arXiv was posted the paper

Posetted trees and Baker-Campbell-Hausdorff product, by Donatella Iacono, Marco Manetti

with the abstract

We introduce the combinatorial notion of posetted trees and we use it in order to write an explicit expression of the Baker-Campbell-Hausdorff formula.

The paper may be relevant (check also the bibliography!) for the subject of writing “finitary“, “noncommutative” BCH formulae, from self-similarity arguments using dilations.

Advertisements

One thought on “Planar rooted trees and Baker-Campbell-Hausdorff formula”

  1. I wonder if it’s the same thing Peter Saveliev was saying?

    http://isomorphism.es/post/24164852462/calculus-is-topology

    actually I thought about it again in an elementary example. Drawing x²/2 for a freshman and showing how the centred derivative is more accurate than the right-hand one which is usually used.

    Put a point, draw two secant lines (equal ± along the abscissa).

    Then the graphically intuitive fact is that, in this 1→1D picture, connecting the two ± points —- which belong to different tangent spaces! —– has “the same” slope as the real tangent. So how to state this in terms of contravariant motion? I.e., motion of the bundles themselves. Because it’s graphically obvious as well that the connected secant-line is not “the” tangent line, since it’s shifted over.

    Anyway, also if you work out the average of left- and right- derivatives (limit definition) then you get a middle term which always cancels. And this reminds me of the ∂²=0 dictum, and I think it’s the same thing (as well as topologically amenable).

    Anyway, then I wondered if it connects to this phenomenon: http://isomorphism.es/post/47732865342/product-rule-with-shapes

    BTW, currently my analogy for top / diff top / riemannian\curvature is this:

    topology = C⁰
    diff top = C¹
    curvature = C²

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s