We study perfect matchings, or close-packed dimer coverings, of finite sections the eleven Archimedean lattices and give a constructive proof showing that any two matchings can be transformed into each other using small sets local ring-exchange moves. This result has direct consequences for formulating quantum models with resonating valence bond ground state, i.e., superposition all coverings c...

In this paper, a local approach to the concept of Hudetz $g$-entropy is presented. The introduced concept is stated in terms of Hudetz $g$-entropy. This representation is based on the concept of $g$-ergodic decomposition which is a result of the Choquet's representation Theorem for compact convex metrizable subsets of locally convex spaces.

This paper provides a review on major ergodic features of semi-independent hyper MV {algebra dynamical systems. Theorems are presentedto make contribution to calculate the entropy. Particularly, it is proved that thetotal entropy of those semi-independent hyper MV {algebra dynamical systemsthat have a generator can be calculated with respect to their generator ratherthan considering all the par...