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    JCT
    2007
    94views more  JCT 2007»
    A bijection between 2-triangulations and pairs of non-crossing Dyck paths
    13 years 11 months ago
    A bijection between 2-triangulations and pairs of non-crossing Dyck paths
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    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
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    JCT
    2007
    142views more  JCT 2007»
    Graphs that triangulate a given surface and quadrangulate another surface
    13 years 11 months ago
    Graphs that triangulate a given surface and quadrangulate another surface
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    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
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    JCT
    2007
    149views more  JCT 2007»
    Weighted forms of Euler's theorem
    13 years 11 months ago
    Weighted forms of Euler's theorem
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    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
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    JCT
    2007
    85views more  JCT 2007»
    Irreducible collineation groups with two orbits forming an oval
    13 years 11 months ago
    Irreducible collineation groups with two orbits forming an oval
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    Angela Aguglia, Arrigo Bonisoli, Gábor Korc...
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    JCT
    2007
    90views more  JCT 2007»
    Overpartitions, lattice paths, and Rogers-Ramanujan identities
    13 years 11 months ago
    Overpartitions, lattice paths, and Rogers-Ramanujan identities
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    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
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    JCT
    2007
    79views more  JCT 2007»
    Generalization of Stanley's monster reciprocity theorem
    13 years 11 months ago
    Generalization of Stanley's monster reciprocity theorem
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    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
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    JCT
    2007
    74views more  JCT 2007»
    Linear algebra approach to geometric graphs
    13 years 11 months ago
    Linear algebra approach to geometric graphs
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    Rom Pinchasi
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    JCT
    2007
    65views more  JCT 2007»
    Paths with two blocks in n-chromatic digraphs
    13 years 11 months ago
    Paths with two blocks in n-chromatic digraphs
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    Louigi Addario-Berry, Frédéric Havet...
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    JCT
    2007
    82views more  JCT 2007»
    A new generalization of Mantel's theorem to k-graphs
    13 years 11 months ago
    A new generalization of Mantel's theorem to k-graphs
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    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
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    JCT
    2007
    77views more  JCT 2007»
    Exponentially many 5-list-colorings of planar graphs
    13 years 11 months ago
    Exponentially many 5-list-colorings of planar graphs
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    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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