Embeddability of the combinohedron

Let e 1,…,e m be m different symbols, let r 1⩾⋯⩾r m be positive integers, and let n=∑ i=1 mr i . The combinohedron, denoted by C(r 1,…,r m) , is the loopless graph whose vertices are the n-tuples in which the symbol e i appears exactly r i times, and where an edge joins two vertices if and only if o...

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Bibliographic Details
Published inDiscrete mathematics Vol. 254; no. 1; pp. 473 - 483
Main Authors Ramı́rez Alfonsı́n, J.L., Romero, David
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 10.06.2002
Elsevier
Subjects
Applied sciences
Combinohedron
Computer science; control theory; systems
Cubic lattice
Embeddings
Exact sciences and technology
Information retrieval. Graph
Multinomial lattice
Permutohedron
Root lattice
Theoretical computing
05C10
05C45
Embeddings
Cubic lattice
Permutohedron
Multinomial lattice
Combinohedron
Root lattice
52C07
Cubic lattices
Embedding
Multinomial distribution
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Summary:Let e 1,…,e m be m different symbols, let r 1⩾⋯⩾r m be positive integers, and let n=∑ i=1 mr i . The combinohedron, denoted by C(r 1,…,r m) , is the loopless graph whose vertices are the n-tuples in which the symbol e i appears exactly r i times, and where an edge joins two vertices if and only if one can be transformed into the other by interchanging two adjacent entries. The graph known as permutohedron is a particular case of the combinohedron. Here, we extend to the combinohedron some results on embeddability of the permutohedron.
ISSN:0012-365X
1872-681X
DOI:10.1016/S0012-365X(01)00298-9