Realization of the Stasheff polytope

By Jean-Louis Loday. 2002

210 citations recorded by the source corpus.

We propose a simple formula for the coordinates of the vertices of the Stasheff polytope (alias associahedron) and we compare it to the permutohedron.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/76646c87337fcc2094d6fdd37d830a9659503897

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

Citations in the corpus

Coxeter submodular functions and deformations of Coxeter permutahedra (2019, background): “[28] In type B, a particular choice of Coxeter element gives Bott and Taubes’s cyclohedron, which originally arose in knot theory.”
Hopf Monoids and Generalized Permutahedra (2017, background): “Since every linear order ` on a finite set |I| has an order-preserving bijection into {1, . . . , |I|}, every Loday associahedron in RI is quasinormally equivalent to the standard Loday associahedron an for n = |I|.”
1-efficient triangulations and the index of a cusped hyperbolic 3-manifold (2013, background): “The cellular decomposition of the polytope Kn 2 (and in particular, its 2–skeleton) is discussed at length in the above references and also in [34].”
A link surgery spectral sequence in monopole Floer homology (2009, background): “For Kn as a convex hull, see [16] and [7].”
Associahedra for finite‐type cluster algebras and minimal relations between g‐vectors (2019, background): “Its realizations can be classified into three species: the secondary polytopes [13, 41], the g -vectors realizations [46, 49, 50, 60, 61, 79, 86, 87] and the d-vector realizations [25, 28].”
Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups (2006, background): “More recently, Loday [90] and Postnikov [99] have constructed geometric realizations.”
Subword complexes, cluster complexes, and generalized multi-associahedra (2011, background): “This simplicial complex is the boundary complex of the dual associahedron [13, 22, 25, 26, 37, 38], we refer to the recent book [39] for a detailed treatment of the history”
Cambrian Lattices (2004, unknown): “Stasheﬀ and Schnider [32] gave a realization of the type-A associahedron by specifying facet hyperplanes, and Loday [20] determined the vertices of this realization.”
Permutohedra, Associahedra, and Beyond (2005, unknown): “e w( ) (1 e w( 1) ) (1 e w( n) ) ; where L be the root lattice.”
Permutahedra and generalized associahedra (2007, background): “Loday [13], and is often referred to as Loday’s realization.”
The diameter of associahedra (2012, background): “On the diameter of other flip-graphs Along with the many constructions of associahedra [1, 3, 4, 9, 11, 14, 17] that followed the ones by Mark Haiman and Carl Lee, several generalizations of these polytopes have been discovered [1, 2, 6, 8, 9].”
Convex Hull Realizations of the Multiplihedra (2007, unknown): “Thanks to XY-pic for the diagrams.”