The Contact Polytope of the Leech Lattice

Sikirić, Mathieu Dutour; Schürmann, Achill; Vallentin, Frank

doi:10.1007/s00454-010-9266-z

Cited by 5 publications

(2 citation statements)

References 14 publications

(16 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Yet another is a storing system for keeping a dual description that may be reused, and this again depends on some heuristics. The method has been applied successfully on numerous problems (Dutour Sikirić et al., , , ) and here.…”

Section: Methodsmentioning

confidence: 99%

Enumeration of the facets of cut polytopes over some highly symmetric graphs

Deza¹,

Sikirić

2015

Int Trans Operational Res

Self Cite

View full text Add to dashboard Cite

We report here a computation giving the complete list of facets for the cut polytopes over several very symmetric graphs with 15-30 edges, includingMöbius ladder M 14 , dodecahedron, Heawood, and Petersen graphs. For K 8 , it shows that the huge list of facets of the cut polytope CUTP 8 and cut cone CUT 8 , given in the literature is complete. We also confirm the conjecture that any facet of CUTP 8 is adjacent to a triangle facet. The lists of facets for K 1,l,m with (l, m) = (4, 4), (3, 5), (3, 4) solve problems in the quantum information theory.

show abstract

Section: Methodsmentioning

confidence: 99%

Enumeration of the facets of cut polytopes over some highly symmetric graphs

Deza¹,

Sikirić

2015

Int Trans Operational Res

Self Cite

View full text Add to dashboard Cite

show abstract

“…In order to compute the facets of the polytope, we used the recursive adjacency decomposition technique. This method has been used for many different computations and is explained in [2,6,10,20]. The idea of the adjacency decomposition technique is to compute one facet and from this facet to compute the adjacent facets.…”

Section: Dual Description Algorithmsmentioning

confidence: 99%