Branched polymers and hyperplane arrangements (2009)
Meszaros, Karola, Postnikov, Alexander
We generalize the construction of connected branched polymers and the notion of the volume of the space of connected branched polymers studied by Kenyon and Winkler to any central linear hyperplane...
Root polytopes, triangulations, and the subdivision algebra, II (2009)
The type C_n full root polytope is the convex hull in R^n of the origin and the points e_i-e_j, e_i+e_j, 2e_k for 1
Root polytopes, triangulations, and the subdivision algebra, I (2009)
The type A_n full root polytope is the convex hull in R^{n+1} of the origin and the points e_i-e_j for 1
Chip-Firing and Rotor-Routing on Directed Graphs (2008)
Holroyd, Alexander E., Levine, Lionel, Meszaros, Karola, Peres, Yuval, Propp, James, Wilson, David B.
We give a rigorous and self-contained survey of the abelian sandpile model and rotor-router model on finite directed graphs, highlighting the connections between them. We present several intriguing...
On the number of genus one labeled circle trees (2005)
A genus one labeled circle tree is a tree with its vertices on a circle, such that together they can be embedded in a surface of genus one, but not of genus zero. We define an e-reduction process...
Latin squares and their defining sets (2005)
A Latin square $L(n,k)$ is a square of order $n$ with its entries colored with $k$ colors so that all the entries in a row or column have different colors. Let $d(L(n,k))$ be the minimal number of...
On low degree k-ordered graphs (2005)
A simple graph G is k-ordered (respectively, k-ordered hamiltonian) if, for any sequence of k distinct vertices v_1, ..., v_k of G, there exists a cycle (respectively, a hamiltonian cycle) in G...
On 3-regular 4-ordered graphs (2005)
A simple graph $G$ is \textit{k-ordered} (respectively, \textit{k-ordered hamiltonian}), if for any sequence of $k$ distinct vertices $v_1, ..., v_k$ of $G$ there exists a cycle (respectively,...