Asymptotic lengths of permutahedra and associahedra
Daria Poliakova
TL;DR
This paper introduces the concept of asymptotic lengths for families of oriented polytopes and calculates these lengths for permutahedra and associahedra, revealing their asymptotic behaviors.
Contribution
It defines asymptotic lengths for oriented polytopes and determines their values for permutahedra and associahedra with specific orientations.
Findings
Permutahedra with weak order orientations have asymptotic total length 1.
Associahedra with Tamari order orientations have asymptotic total length 1/2.
Abstract
We define asymptotic lengths for families of oriented polytopes. We show that permutahedra with weak order orientations have asymptotic total length 1 and associahedra with Tamari order orientations have asymptotic total length 1/2.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics