The $M$-triangle of generalised non-crossing partitions for the types $E_7$ and $E_8$

Christian Krattenthaler

The $M$-triangle of a ranked locally finite poset $P$ is the generating function $\sum_{u,w\in P} ^{}μ(u,w) x^{\rk u}y^{\rk w}$, where $\mu (.,.)$ is the Möbius function of $P$. We co…