What makes a \(\mathbf D_0\) graph Schur positive?
A fundamental problem in the theory of LLT polynomials is to give a positive combinatorial expansion of these polynomials in terms of Schur functions. The paper under review is an attempt to attack this problem by studying \(D_0\) graphs by developing \textit{S. Fomin} and \textit{C. Greene}'s theory of noncommutative Schur functions [Discrete Math. 193, No. 1--3, 179--200 (1998; Zbl 1011.05062)]. In particular, the author constructed a \(D_0\) graph whose generating functions are not Schur positive. The result is surprisingly contrary to the speculation that \(D_0\) graphs always have Schur positive generating functions.
scientific article; zbMATH DE number 6656216
scientific article