A new approach to Macaulay posets

Bezrukov, Sergei L.; Piotrowski, Victor; Pfaff, Thomas J.

doi:10.1016/s0097-3165(03)00017-7

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The Chain Hypergraphs1

Introduction1

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2007

2018

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Cited by 3 publications

(2 citation statements)

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“…The hypergraph P k,t for given k > 1 and t 1 has the following -sequence: The MRI-order P n k,t for the cartesian powers of the chain hypergraphs follows from a general construction in [8]. For x ∈ V P k,t denote x = x mod k and x = x/k .…”

Section: The Chain Hypergraphsmentioning

confidence: 99%

On partitioning of hypergraphs

Bezrukov

Battiti

2007

Discrete Mathematics

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We study edge-isoperimetric problems (EIP) for hypergraphs and extend some technique in this area from graphs to hypergraphs. In particular, we establish some new results on a relationship between the EIP and some extremal poset problems, and apply them to obtain an exact solution of the EIP for certain hypergraph families. We also show how to solve the EIP on hypergraphs in some cases when the link to posets does not work. Another outcome of our results is a new series of hypergraphs admitting nested solutions in the EIP.

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Section: The Chain Hypergraphsmentioning

confidence: 99%

On partitioning of hypergraphs

Bezrukov

Battiti

2007

Discrete Mathematics

Self Cite

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“…It turns out that just a few different optimal orders are discovered for the EIPis. Some of them are proved to work just for a few graphs [2,4]. This leaves the lexicographic order to work in most of known cases.…”

Section: Introductionmentioning

confidence: 99%