Families of m-convex polygons: m = 2

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dc.creatorJames, W. R. G.
dc.creatorJensen, I.
dc.creatorGuttmann, A. J.
dc.date2007-10-25
dc.date.accessioned2026-07-07T08:38:33Z
dc.date.available2026-07-07T08:38:33Z
dc.descriptionPolygons are described as almost-convex if their perimeter differs from the perimeter of their minimum bounding rectangle by twice their `concavity index', $m$. Such polygons are called \emph{$m$-convex} polygons and are characterised by having up to $m$ indentations in the side. We use a `divide and conquer' approach, factorising 2-convex polygons by extending a line along the base of its indents. We then use the inclusion-exclusion principle, the Hadamard product and extensions to known methods to derive the generating functions for each case.
dc.description53 pages
dc.identifierhttps://arxiv.org/abs/0710.4606
dc.identifierhttp://arxiv.org/abs/0710.4606
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/140769
dc.subjectCombinatorics
dc.subject05A15
dc.titleFamilies of m-convex polygons: m = 2
dc.typetext

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