In mathematics, the permutohedron (also spelled permutahedron) of order n is an (n − 1)-dimensional polytope embedded in an n-dimensional space. Its vertex...

Like the cube, it can tessellate (or "pack") 3-dimensional space, as a permutohedron. The truncated octahedron was called the "mecon" by Buckminster Fuller...

represented as the vertices of a permutohedron, and the dichotomies on this same set as the facets of the permutohedron. In this geometric representation...

elements. Equivalently, this algorithm finds a Hamiltonian cycle in the permutohedron, a polytope whose vertices represent permutations and whose edges represent...

inversion sets ordered by the subset relation forms the skeleton of a permutohedron. If a permutation is assigned to each inversion set using the place-based...

Just as the truncated octahedron is the permutohedron of order 4, the omnitruncated 5-cell is the permutohedron of order 5. The omnitruncated 5-cell is...

geometric combinatorics. Special polytopes are also considered, such as the permutohedron, associahedron and Birkhoff polytope. Topological combinatorics What...

geometric combinatorics. Special polytopes are also considered, such as the permutohedron, associahedron and Birkhoff polytope. Combinatorial analogs of concepts...

A Hamiltonian path in the permutohedron, a Cayley graph of the symmetric group with Coxeter generators...

Steinhaus–Johnson–Trotter algorithm for finding a Hamiltonian path in a permutohedron Subhamiltonian graph, a subgraph of a planar Hamiltonian graph Tait's...

tessellate space. The truncated octahedron contains 14 faces, is the permutohedron of order four, and the only Archimedean solid to tessellate space. The...

9-orthoplex, t0,1,2,3,4,5,6,7{37,4} The omnitruncated 8-simplex is the permutohedron of order 9. The omnitruncated 8-simplex is a zonotope, the Minkowski...

partitions of a squarefree number or the faces of all dimensions of a permutohedron. Weak orderings arrange their elements into a sequence allowing ties...

(Acronym: gotaf) (Jonathan Bowers) The omnitruncated 6-simplex is the permutohedron of order 7. The omnitruncated 6-simplex is a zonotope, the Minkowski...

with all reflective mirrors active. The omnitruncated 7-simplex is the permutohedron of order 8. The omnitruncated 7-simplex is a zonotope, the Minkowski...

6-orthoplex, t0,1,2,3,4{34,4}, . The omnitruncated 5-simplex is the permutohedron of order 6. It is also a zonotope, the Minkowski sum of six line segments...

problem Permutation graph Permutation pattern Permutation polynomial Permutohedron Rencontres numbers Robinson–Schensted correspondence Sum of permutations:...

segments), the omnitruncated 5-cell, and the truncated 24-cell. Every permutohedron is a zonotope. Fix a zonotope Z {\displaystyle Z} defined from the set...

is given by the Catalan numbers. The corresponding numbers for the permutohedron are respectively the ordered Bell numbers and the factorials. As well...

all triangle faces Steffen's polyhedron – A flexible tetradecahedron Permutohedron – A polyhedron that can be defined in any dimension and equals the truncated...

representations include, among others Four color theorem, Young tableau, Permutohedron, Graph theory, Partition of a set. Brain imaging experiments conducted...

An important special case of a partial cube is the skeleton of the permutohedron, a graph in which vertices represent permutations of a set of ordered...

that computes the maximum flow in a flow network. Birkhoff algorithm Permutohedron Stable matching polytope Ziegler, Günter M. (2007) [2006], Lectures...

Flip graph, a generalisation of the 1-skeleton of the associahedron. Permutohedron, a polytope that is defined from commutativity in a similar way to the...

Sam; Spingarn, Ethan (2023), Unit-interval parking functions and the permutohedron, arXiv:2305.15554; Meyles et al credit the connection between parking...

cyclohedron can be recovered by removing some of the facets of the permutohedron. The graph made up of the vertices and edges of the d {\displaystyle...

p > 6. The 3-color tiling is a tessellation generated by the order-3 permutohedrons. A chamfered hexagonal tiling replaces edges with new hexagons and transforms...

The factorial numbers of a given length form a permutohedron when ordered by the bitwise ≤ {\displaystyle \leq } relation These are the right inversion...

Weaire–Phelan structure appears to be the best. The honeycomb represents the permutohedron tessellation for 3-space. The coordinates of the vertices for one octahedron...

higher dimensions include the d-simplex, hypercube, associahedron, permutohedron, and all omnitruncated polytopes. Micha Perles conjectured that a simple...