A distributed computation is usually modeled as a finite partially ordered set (poset) of events. Many operations on this poset require computing meets and joins of subsets of events. The lattice of normal cuts of a poset is the smallest lattice that embeds the poset such that all meets and joins are defined. In this paper, we propose new algorithms to construct or enumerate the lattice of norm...

We provide a combinatorial recipe for constructing all posets of height at most two which the corresponding type-A Lie poset algebra is contact. In case that such are connected, discrete Morse theory argument establishes posets' simplicial realizations contractible. It follows from cohomological result Coll and Gerstenhaber on semi-direct products contact algebras absolutely rigid.

A subset S of a poset (partially ordered set) is convex if and only if S contains every poset element which is between any two elements in S. Poset convex subsets arise in applications that involve precedence constraints, such as in project scheduling, production planning, and assembly line balancing. We give a strongly polynomial time algorithm which, given a poset and element weights (of arbi...

Poset game, which includes some famous games. e.g., Nim and Chomp as sub-games, is an important two-player impartial combinatorial game. The rule of the game is as follows: For a given poset (partial ordered set), each player intern chooses an element and the selected element and it’s descendants (elements succeeding it) are all removed from the poset. A player who choose the last element is th...

Hierarchical data, such as Partially Ordered Set (POSET) is tremendously used in relational databases, especially in data mining and data warehouse based-applications. Unfortunately, SQL (Structured Query Language) does not effectively support hierarchical data structure to manage this sort of data, for example, in Oracle, a CONNECT BY operator is used to query data organized into trees, howeve...