Chromatic polynomial and the weight system
Sergei Lando
HSE University, Moscow, Russia; Skolkovo Institute of Science and Technology, Moscow, RussiaZhuoke Yang
Beijing Institute of Mathematical Sciences and Applications, Beijing, P. R. China

Abstract
In a recent paper by M. Kazarian and the second author, a recurrence for the Lie algebras weight systems has been suggested; the recurrence allows one to construct the universal weight system. The construction is based on an extension of the weight systems to permutations. Another recent paper, by M. Kazarian, N. Kodaneva, and the first author, shows that under the substitution , for the Casimir elements , the leading term in of the value of the universal weight system becomes the chromatic polynomial of the intersection graph of the chord diagram. The present paper establishes a similar result for the universal weight system. That is, we show that the leading term of the universal weight system also becomes the chromatic polynomial under a specific substitution.
Cite this article
Sergei Lando, Zhuoke Yang, Chromatic polynomial and the weight system. Ann. Inst. Henri Poincaré Comb. Phys. Interact. (2025), published online first
DOI 10.4171/AIHPD/208