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JCT
2007
94views more  JCT 2007»
9 years 11 months ago
A bijection between 2-triangulations and pairs of non-crossing Dyck paths
A k-triangulation of a convex polygon is a maximal set of diagonals so that no k + 1 of them mutually cross in their interiors. We present a bijection between 2-triangulations of a...
Sergi Elizalde
JCT
2007
142views more  JCT 2007»
9 years 11 months ago
Graphs that triangulate a given surface and quadrangulate another surface
We show that for any closed surface F with χ(F) −4 (or χ(F) −2), there exist graphs that triangulate the torus or the Klein bottle (or the projective plane) and that quadran...
Yusuke Suzuki
JCT
2007
149views more  JCT 2007»
9 years 11 months ago
Weighted forms of Euler's theorem
In answer to a question of Andrews about finding combinatorial proofs of two identities in Ramanujan’s “lost” notebook, we obtain weighted forms of Euler’s theorem on part...
William Y. C. Chen, Kathy Q. Ji
JCT
2007
85views more  JCT 2007»
9 years 11 months ago
Irreducible collineation groups with two orbits forming an oval
Angela Aguglia, Arrigo Bonisoli, Gábor Korc...
JCT
2007
90views more  JCT 2007»
9 years 11 months ago
Overpartitions, lattice paths, and Rogers-Ramanujan identities
We define the notions of successive ranks and generalized Durfee squares for overpartitions. We show how these combinatorial statistics give extensions to overpartitions of combin...
Sylvie Corteel, Olivier Mallet
JCT
2007
79views more  JCT 2007»
9 years 11 months ago
Generalization of Stanley's monster reciprocity theorem
By studying the reciprocity property of linear Diophantine systems in light of Malcev-Neumann series, we present in this paper a new approach to and a generalization of Stanley’s...
Guoce Xin
JCT
2007
65views more  JCT 2007»
9 years 11 months ago
Paths with two blocks in n-chromatic digraphs
Louigi Addario-Berry, Frédéric Havet...
JCT
2007
82views more  JCT 2007»
9 years 11 months ago
A new generalization of Mantel's theorem to k-graphs
Let the k-graph Fank consist of k edges that pairwise intersect exactly in one vertex x, plus one more edge intersecting each of these edges in a vertex different from x. We prov...
Dhruv Mubayi, Oleg Pikhurko
JCT
2007
77views more  JCT 2007»
9 years 11 months ago
Exponentially many 5-list-colorings of planar graphs
We prove that every planar graph with n vertices has at least 2n/9 distinct list-colorings provided every vertex has at least five available colors. © 2006 Elsevier Inc. All rig...
Carsten Thomassen
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