论文标题
字符和色度对称功能
Characters and chromatic symmetric functions
论文作者
论文摘要
令$ p $为poset，$ inc（p）$其不可比程图，$ x_ {inc（p）} $由斯坦利（Stanley）在{\ em adv中定义的相应的色度对称函数。 Math。}，{\ bf 111}（1995）pp。〜166--194。 $ p $的某些条件意味着标准对称函数库中的$ x_ {inc（p）} $的扩展产生了具有简单组合解释的系数。通过将这些系数表示为角色评估，我们将其中几种解释扩展到{\ em all} posets $ p $。后果包括对完全非负矩阵的永久性和其他内在物的新组合解释，以及Shareshian-wachs彩色准对象函数中基本系数的总和$ x_ {inc（p），q}，q} $当$ p $是一个单位间隔订单。
Let $P$ be a poset, $inc(P)$ its incomparability graph, and $X_{inc(P)}$ the corresponding chromatic symmetric function, as defined by Stanley in {\em Adv. Math.}, {\bf 111} (1995) pp.~166--194. Certain conditions on $P$ imply that the expansions of $X_{inc(P)}$ in standard symmetric function bases yield coefficients which have simple combinatorial interpretations. By expressing these coefficients as character evaluations, we extend several of these interpretations to {\em all} posets $P$. Consequences include new combinatorial interpretations of the permanent and other immanants of totally nonnegative matrices, and of the sum of elementary coefficients in the Shareshian-Wachs chromatic quasisymmetric function $X_{inc(P),q}$ when $P$ is a unit interval order.
