2024/11/02 by Sergei K. Lando, Lando, Sergei, Zhuoke Yang +1
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Mathematical functions and polynomials
paper · pdf · doi:10.48550/arxiv.2411.01128
openalex publication_date 2024/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a recent paper by M.Kazarian and the second author, a recurrence for the Lie algebras \mathfrakso(N) weight systems has been suggested; the recurrence allows one to construct the universal \mathfrakso weight system. The construction is based on an extension of the \mathfrakso weight systems to permutations. Another recent paper, by M. Kazarian, N. Kodaneva, and the first author, shows that under the substitution Cm=xNm-1, m=1,2,…, for the Casimir elements Cm, the leading term in N of the value of the universal \mathfrakgl weight system becomes the chromatic polynomial of the intersection graph of the chord diagram. In the present paper, we establish a similar result for the universal \mathfrakso weight system. That is, we show that the leading term of the universal \mathfrakso weight system also becomes the chromatic polynomial under a specific substitution.