A simple permutoassociahedron

Geometrical Realisations of the Simple Permutoassociahedron by Minkowski sums

This paper offers a geometrical realisation of simple permutoassociahedra, which has significant importance serving as a topological proof of Mac Lane's coherence. We introduce a family of $n$-polytopes, $PA_{n,c}$, obtained by Minkowski sums such that each summand yields to the appropriate facet of the resulting sum. Additionally, it leads to the correlation between Minkowski sums and truncations of permutohedron, which implicitly gives a general procedure for geometrical Minkowski-construction of any permutonestohedron.

某些广义关联多面体的面着色的色数

Chromatic numbers for facet colouring of some generalised associahedra

本文研究了几类广义关联多面体面着色的色数，给出了置换多面体、关联多面体和简单置换关联多面体的精确值，并建立了环面多面体和星形多面体的上下界及其渐近值。