Linear extension majority cycles for small (n⩽9) partial orders

Extending Partial Orders to Dense Linear Orders

Aggregate Functions, Conservative Extension, and Linear Orders

1 Summary Practical database query languages are usually equipped with some aggregate functions. For example, \\nd mean of column" can be expressed in SQL. However, the manner in which aggregate functions were introduced in these query languages leaves something to be desired. Breazu-Tannen, Buneman, and Wong 3] introduced a nested relational language NRC(=) based on monads 16, 24] and structur...

Coloring linear orders with Rado's partial order

Let 1R be the preorder of embeddability between countable linear orders colored with elements of Rado’s partial order (a standard example of a wqo which is not a bqo). We show that 1R has fairly high complexity with respect to Borel reducibility (e.g. if P is a Borel preorder then P ≤B 1R), although its exact classification remains open.

Partial Orders, Event Structures and Linear Strategies

We introduce a Game Semantics where strategies are partial orders, and composition is a generalization of the merging of orders. Building on this, to bridge between Game Semantics and Concurrency, we explore the relation between Event Structures and Linear Strategies. The former are a true concurrency model introduced by Nielsen, Plotkin, Winskel, the latter a family of linear innocent strategi...

On Unimodality for Linear Extensions of Partial Orders

R. Rivest has recently proposed the following intriguing conjecture: Let x* denote an arbitrary fixed element in an n-element partially ordered set P, and for each k in {1, 2, , n let Nk be the number of order-preserving maps from P onto {1, 2,..., n} that map x* into k. Then the sequence N1,'' ', N,, is unimodal. This note proves the conjecture for the special case in which P can be covered by...