5 papers
Parity Property of Hexagonal Sliding Puzzles
Ray Karpman, Erika Roldan
We study the puzzle graphs of hexagonal sliding puzzles of various shapes and with various numbers of holes. The puzzle graph is a combinatorial model which captures the solvabilit…
Isotopy graphs of Latin tableaux
R. Karpman, É. Roldán
Latin tableaux are a generalization of Latin squares, which first appeared in the early 2000's in a paper of Chow, Fan, Goemans, and Vondrák. Here, we extend the notion of isotopy,…
Topology and local geometry of the Eden model
Fedor Manin, Erika Roldan, Benjamin Schweinhart
The Eden cell growth model is a simple discrete stochastic process which produces a "blob" in : start with one cube in the regular grid, and at each time step add a n…
Topology of random 2-dimensional cubical complexes
Matthew Kahle, Elliot Paquette, Érika Roldán
We study a natural model of random 2-dimensional cubical complex which is a subcomplex of an n-dimensional cube, and where every possible square -face is included independently…
Art gallery problem with rook and queen vision
Hannah Alpert, Érika Roldán
How many chess rooks or queens does it take to guard all the squares of a given polyomino, the union of square tiles from a square grid? This question is a version of the art galle…