JCT

2007

13 years 8 months ago
2007

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...

JCT

2007

13 years 8 months ago
2007

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...

JCT

2007

13 years 8 months ago
2007

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...

JCT

2007

13 years 9 months ago
2007

JCT

2007

13 years 9 months ago
2007

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...

JCT

2007

13 years 9 months ago
2007

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...

JCT

2007

13 years 9 months ago
2007

JCT

2007

13 years 9 months ago
2007

JCT

2007

13 years 9 months ago
2007

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...

JCT

2007

13 years 9 months ago
2007

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...