COMBINATORICS
2007
13 years 4 months ago
2007
COMBINATORICS
2007
13 years 4 months ago
2007
In this paper, we revisit the enumeration of directed animals using gas models. We show that there exists a natural construction of random directed animals on any directed graph t...
COMBINATORICS
2007
13 years 4 months ago
2007
We enumerate rooted triangulations of a sphere with multiple holes by the total number of edges and the length of each boundary component. The proof relies on a combinatorial iden...
COMBINATORICS
2007
13 years 4 months ago
2007
We define a higher spin alternating sign matrix to be an integer-entry square matrix in which, for a nonnegative integer r, all complete row and column sums are r, and all partia...
COMBINATORICS
2007
13 years 4 months ago
2007
Let G be a simple balanced bipartite graph on 2n vertices, δ = δ(G)/n, and ρ0 = δ+ √ 2δ−1 2 . If δ ≥ 1/2 then G has a ρ0n -regular spanning subgraph. The statement is...
COMBINATORICS
2007
13 years 4 months ago
2007
The idea of graph compositions, which was introduced by A. Knopfmacher and M. E. Mays, generalizes both ordinary compositions of positive integers and partitions of finite sets. ...
COMBINATORICS
2007
13 years 4 months ago
2007
Sylvester’s identity is a classical determinantal identity with a straightforward linear algebra proof. We present combinatorial proofs of several non-commutative extensions, an...
COMBINATORICS
2007
13 years 4 months ago
2007
In this paper, we derive an interesting identity from the Rogers-Fine identity by applying the q-exponential operator method.
COMBINATORICS
2007
13 years 4 months ago
2007
A hypermap is (hypervertex-) bipartite if its hypervertices can be 2-coloured in such a way that “neighbouring” hypervertices have different colours. It is bipartiteuniform i...
COMBINATORICS
2007
13 years 4 months ago
2007
We determine the exact and asymptotic number of unlabeled outerplanar graphs. The exact number gn of unlabeled outerplanar graphs on n vertices can be computed in polynomial time,...