A natural, but slowly emerging program. In his PhD thesis prepared under the supervision of
Graham Higman and defended in 1965 [123], and in the article that followed [124], FA …

In this paper, we use subword complexes to provide a uniform approach to finite-type cluster
complexes and multi-associahedra. We introduce, for any finite Coxeter group and any …

We interpret the support $\tau $-tilting complex of any gentle bound quiver as the non-
kissing complex of walks on its blossoming quiver. Particularly relevant examples were …

Abstract We survey Jean-Louis Loday's vertex description of the associahedron, and its far
reaching influence in combinatorics, discrete geometry, and algebra. We present in …

A survey is given of recent results on fine zonotopal tilings by cubes (briefly, cubillages) of
cyclic zonotopes. The main interest of this theory is that it is interrelated with the theory of …

Cambrian trees are oriented and labeled trees which fulfill local conditions around each
node generalizing the classical conditions for binary search trees. Similar to binary trees for …

In this paper, we exploit the combinatorics and geometry of triangulations of products of
simplices to derive new results in the context of Catalan combinatorics of $\nu $-Tamari …

For each meet-semilattice M, we define an operator Pop M: M→ M by Pop M (x)=⋀({y∈ M:
y⋖ x}∪{x}). When M is the right weak order on a symmetric group, Pop M is the pop-stack …

We generalize the brick polytope of V. Pilaud and F. Santos to spherical subword complexes
for finite Coxeter groups. This construction provides polytopal realizations for a certain class …

It is shown that higher Bruhat orders admit a decomposition into a higher Tamari order, the
corresponding dual Tamari order, and a''mixed order''. We describe simplex equations …