Amenable Orders Associated with Inverse Transversals

Automorphism Groups of Countably Categorical Linear Orders are Extremely Amenable

We show that the automorphism groups of countably categorical linear orders are extremely amenable. Using methods of Kechris, Pestov, and Todorcevic, we use this fact to derive a structural Ramsey theorem for certain families of finite ordered structures with finitely many partial equivalence relations with convex classes.

factors associated with medical orders’ compliance among hyperlipidemic patients

background: coronary artery diseases are one of the most important issues in health and social problems. one of the amendable risk factors in development of these diseases is high cholesterol which can be modified through correction of lifestyle (diet change, playing sports, and usage of lipid‑lowering drugs). patients’ compliance to therapeutic programs is the most important element to achieve...

Zonotopes associated with higher Bruhat orders

Equivalence Relations with Amenable Leaves Need Not Be Amenable

There are two notions of amenability for discrete equivalence relations. The \global" amenability (which is usually referred to just as \amenability") is the property of existence of leafwise invariant means, which, by a theorem of Connes{Feldman{Weiss, is equivalent to hyperrniteness, or, to being the orbit equivalence relation of a Z-action. The notion of \local" amenability applies to equiva...

Latin Squares with No Transversals

A k-plex in a latin square of order n is a selection of kn entries that includes k representatives from each row and column and k occurrences of each symbol. A 1-plex is also known as a transversal. It is well known that if n is even then Bn, the addition table for the integers modulo n, possesses no transversals. We show that there are a great many latin squares that are similar to Bn and have...