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It should be pointed out that di is a shorthand notation for dvi . • Page 3, definition of ”fire”: You write: ”An active vertex v can fire, resulting in a new chip configuration σ′ obtained by moving… (More)

- Karola Mészáros
- Discrete Mathematics
- 2008

A simple graph G is k-ordered (respectively, k-ordered hamiltonian), if for any sequence of k distinct vertices v1, . . . , vk of G there exists a cycle (respectively, hamiltonian cycle) in G… (More)

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… (More)

- Karola Mészáros
- 2009

The type An root polytope P(An ) is the convex hull in R of the origin and the points ei − ej for 1 ≤ i < j ≤ n + 1. Given a tree T on the vertex set [n + 1], the associated root polytope P(T ) is… (More)

- Karola Mészáros
- 2009

The type Cn root polytope P(C n ) is the convex hull in R of the origin and the points ei−ej , ei+ej , 2ek for 1 ≤ i < j ≤ n, k ∈ [n]. Given a graph G, with edges labeled positive or negative,… (More)

- Karola Mészáros
- Discrete Mathematics
- 2008

A simple graph G is k-ordered (respectively, k-ordered hamiltonian) if, for any sequence of k distinct vertices v1, . . . , vk of G, there exists a cycle (respectively, a hamiltonian cycle) in G… (More)

- Louis J. Billera, Lionel Levine, Karola Mészáros
- ArXiv
- 2013

We give a bijection between permutations of 1, . . . , 2n and certain pairs of Dyck paths with labels on the down steps. The bijection arises from a game in which two players alternate selecting from… (More)

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… (More)

- Karola Mészáros, Greta Panova, Alexander Postnikov
- Electr. J. Comb.
- 2014

We study multiplication of any Schubert polynomial Sw by a Schur polynomial sλ (the Schubert polynomial of a Grassmannian permutation) and the expansion of this product in the ring of Schubert… (More)

- Karola Mészáros
- Electr. J. Comb.
- 2013

The number of regions of the type Cn Shi arrangement in Rn is (2n + 1)n. Strikingly, no bijective proof of this fact has been given thus far. The aim of this paper is to provide such a bijection and… (More)