368 research outputs found
The poset of graphs ordered by induced containment
I would like to express my gratitude to the anonymous referees for their extremely useful comments and corrections which greatly improved the paper.Peer reviewedPreprintPostprin
Pseudograph associahedra
Given a simple graph G, the graph associahedron KG is a simple polytope whose
face poset is based on the connected subgraphs of G. This paper defines and
constructs graph associahedra in a general context, for pseudographs with loops
and multiple edges, which are also allowed to be disconnected. We then consider
deformations of pseudograph associahedra as their underlying graphs are altered
by edge contractions and edge deletions.Comment: 25 pages, 22 figure
Realizability of Polytopes as a Low Rank Matrix Completion Problem
This article gives necessary and sufficient conditions for a relation to be
the containment relation between the facets and vertices of a polytope. Also
given here, are a set of matrices parameterizing the linear moduli space and
another set parameterizing the projective moduli space of a combinatorial
polytope
Some open problems on permutation patterns
This is a brief survey of some open problems on permutation patterns, with an
emphasis on subjects not covered in the recent book by Kitaev, \emph{Patterns
in Permutations and words}. I first survey recent developments on the
enumeration and asymptotics of the pattern 1324, the last pattern of length 4
whose asymptotic growth is unknown, and related issues such as upper bounds for
the number of avoiders of any pattern of length for any given . Other
subjects treated are the M\"obius function, topological properties and other
algebraic aspects of the poset of permutations, ordered by containment, and
also the study of growth rates of permutation classes, which are containment
closed subsets of this poset.Comment: 20 pages. Related to upcoming talk at the British Combinatorial
Conference 2013. To appear in London Mathematical Society Lecture Note Serie
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