We study and classify faithfully balanced modules for the algebra of triangular n by matrices more generally Nakayama algebras. The theory extends known results about tilting modules, which are classified binary trees, counted with Catalan numbers. number is a 2-factorial number. Among them n! indecomposable summands, can be interleaved trees or increasing trees.

Combinatorial Designs, also known as experimental designs, historically first were used in agriculture. With the advent of electronic computers together with the significant advancement of combinatorics, combinatorial structures have become an often used means in computer science. At present, massively parallel computers become more and more reliable so that they can be used as production syste...