论文标题
向上的代数和色度对称函数
Down-up algebras and chromatic symmetric functions
论文作者
论文摘要
我们通过将其代数与$ q $ -Klyachko代数的路径联系起来，建立了某些色度对称函数之间未发表的线性关系。这种关系中的系数是$ q $ hit的多项式，与Colmenarejo-Morales-Panova的计算方法相反，它们在我们的设置中自然而然地出现在我们的设置中。由于Guay-Paquet的代数是一个淡淡的代数，因此我们能够在后者的背景下利用代数结果并建立组合风味的结果。特别是我们解决了colmenarejo-morales-panova在色度对称函数上的猜想。这涉及斯坦利 - 茎布里奇猜想的阿贝尔案，我们对此进行了简要调查。
We establish Guay-Paquet's unpublished linear relation between certain chromatic symmetric functions by relating his algebra on paths to the $q$-Klyachko algebra. The coefficients in this relations are $q$-hit polynomials, and they come up naturally in our setup as connected remixed Eulerian numbers, in contrast to the computational approach of Colmenarejo-Morales-Panova. As Guay-Paquet's algebra is a down-up algebra, we are able to harness algebraic results in the context of the latter and establish results of a combinatorial flavour. In particular we resolve a conjecture of Colmenarejo-Morales-Panova on chromatic symmetric functions. This concerns the abelian case of the Stanley-Stembridge conjecture, which we briefly survey.
