Removahedral congruences versus permutree congruences
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TLDR
In this article, the permutree fans are realized by a permovahedron constructed from any realization of the braid fan, and the permutahedron can be realized by any permutrees fan.Abstract:
The associahedron is classically constructed as a removahedron, i.e. by deleting inequalities in the facet description of the permutahedron. This removahedral construction extends to all permutreehedra (which interpolate between the permutahedron, the associahedron and the cube). Here, we investigate removahedra constructions for all quotientopes (which realize the lattice quotients of the weak order). On the one hand, we observe that the permutree fans are the only quotient fans realized by a removahedron. On the other hand, we show that any permutree fan can be realized by a removahedron constructed from any realization of the braid fan. Our results finally lead to a complete description of the type cone of the permutree fans.read more
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OUP accepted manuscript
TL;DR: In this paper , a simpler approach to realize quotient fans based on Minkowski sums of elementary polytopes, called shard polytes, which have remarkable combinatorial and geometric properties, was proposed.
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