  In a recent paper Zhuoke Yang, New approaches to ${\mathfrak gl}(N)$ weight
system, Izvestiya Mathematics, 2023, vol. 77:6, 150--166; arXiv:2202.12225
(2022) a construction of a weight system, which unifies ${\mathfrak gl}(N)$
weight systems for $N=1,2,\dots$, has been suggested. The construction is based
on an extension of the ${\mathfrak gl}(N)$ weight systems to permutations. This
universal weight system takes values in the algebra of polynomials ${\mathbb
C}[N;C_1,C_2,\dots]$ in infinitely many variables. We show that under the
substitution $C_m=xN^{m-1}$, $m=1,2,\dots$, the leading term in $N$ of the
value of the universal ${\mathfrak gl}$ weight system becomes the chromatic
polynomial of the intersection graph of the chord diagram. Moreover, we show
that under the substition $C_m=p_m N^{m-1}$, $m=1,2,\dots$, the leading term in
$N$ of the value of the universal ${\mathfrak gl}$ weight system determines a
flitered Hopf algebra homomorphism from the rotational Hopf algebra of
permutations, which we construct in the present paper, to the Hopf algebra of
polynomials ${\mathbb C}[p_1,p_2,\dots]$.
