2024/09/16 by Dakota M. Leonard, Leonard, Dakota M.
Biochemistry, Genetics and Molecular Biology · Materials Science · #Chemical Synthesis and Analysis #Dynamical Systems (math.DS) #FOS: Mathematics #Gene Regulatory Network Analysis #Supramolecular Self-Assembly in Materials
paper · pdf · doi:10.48550/arxiv.2409.10745
openalex publication_date 2024/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
Let G be a discrete, countably infinite group and H a subgroup of G. If H acts continuously on a compact metric space X, then we can induce a continuous action of G on ∏H\backslash GX where H\backslash G is the collection of right-cosets of H in G. This process is known as the co-induction. In this article, we will calculate the maximal pattern entropy of the co-induction. If [G:H] < +∞ we will show that the H action is null if and only if the co-induced action of G is null. Also, we will discuss an example where H is a proper subgroup of G with finite index where the maximal pattern entropy of the H action is equal to the co-induced action of G. If [G:H] = +∞ we will show that the maximal pattern entropy of the co-induction is always +∞ given the H-system is not trivial.