Journal
SELECTA MATHEMATICA-NEW SERIES
Volume 26, Issue 3, Pages -Publisher
SPRINGER INTERNATIONAL PUBLISHING AG
DOI: 10.1007/s00029-020-00562-w
Keywords
-
Categories
Funding
- RSF Grant [16-11-10316]
- Russian Science Foundation [16-11-10316] Funding Source: Russian Science Foundation
Ask authors/readers for more resources
We prove that the generating function for the symmetric chromatic polynomial of all simple graphs is (after an appropriate scaling change of variables) a linear combination of one-part Schur polynomials. This statement immediately implies that it is also a tau-function of the Kadomtsev-Petviashvili integrable hierarchy of mathematical physics. Moreover, we describe a large family of polynomial graph invariants leading to the same tau-function. In particular, we introduce the Abel polynomial for graphs and show this for its generating function. The key point here is a Hopf algebra structure on the space spanned by graphs and the behavior of the invariants on its primitive space.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available