4 papers
Algorithm for computing Representations of the Braid Group and Temperley-Lieb algebra
Yitzchak Shmalo
The braid group appears in many scientific fields and its representations are instrumental in understanding topological quantum algorithms, topological entropy, classification of m…
Combinatorial Proof of Kakutani's Fixed Point Theorem
Yitzchak Shmalo
Kakutani's fixed point theorem is a generalization of Brouwer's fixed point theorem to upper semicontinuous multivalued maps and is used extensively in game theory and other areas…
The K-Theoretic Bulk-Boundary Principle for Dynamically Patterned Resonators
Emil Prodan, Yitzchak Shmalo
Starting from a dynamical system , with a generic topological group, we devise algorithms that generate families of patterns in the Euclidean space, which densely embed…
Combinatorial approach to detection of fixed points, periodic orbits, and symbolic dynamics
Marian Gidea, Yitzchak Shmalo
We present a combinatorial approach to rigorously show the existence of fixed points, periodic orbits, and symbolic dynamics in discrete-time dynamical systems, as well as to find…