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Complexity of chess domination problems
Alexis Langlois-Rémillard, Mia Müßig, Érika Róldan
We study different domination problems of attacking and non-attacking rooks and queens on polyominoes and polycubes of all dimensions. Our main result proves that maximum independe…
Isoperimetric Formulas for Hyperbolic Animals
Erika Roldan, Rosemberg Toala-Enriquez
An animal is a planar shape formed by attaching congruent regular polygons along their edges. In 1976, Harary and Harborth gave closed isoperimetric formulas for Euclidean animals.…
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…
High-dimensional holeyominoes
Greg Malen, Fedor Manin, Erika Roldan
What is the maximum number of holes enclosed by a -dimensional polyomino built of tiles? Represent this number by . Recent results show that converges to…
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 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…