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A noncommutative approach to the Schur positivity of chromatic symmetric functions

open access: yes
26 pages, with an appendix of 6 pagesWe obtain the Schur positivity of spider graphs of the forms $S(a,2,1)$ and $S(a,4,1)$, which are considered to have the simpliest structures for which the Schur positivity was unknown.
Wang, David G. L., Thibon, Jean-Yves
core  

The Kneser chromatic function distinguishes trees

open access: yes
R.P. Stanley defined a invariant for graphs called the chromatic symmetric function and conjectured it is complete invariant for trees. Miezaki et al.
Nishimura, Yusaku
core  

$q$-Chromatic polynomials

open access: yes
We introduce and study a $q$-version of the chromatic polynomial of a given graph $G=(V,E)$, namely, \[ \chi_G^\lambda(q,n) \ := \sum_{\substack{\text{proper colorings}\\ c\,:\,V\to[n]}} q^{ \sum_{ v \in V } \lambda_v c(v) }, \] where $\lambda \in ...
Beck, Matthias   +2 more
core  

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