Frequency estimates for linear extension majority cycles on partial orders

Extending Partial Orders to Dense Linear Orders

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...

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...

Computing the Frequency of Partial Orders

In this paper we will study four algorithms for computing the frequency of a given partial order. Here the frequency of a partial order is the number of standard labellings respecting that partial order. We formulate frequency computation of partial orders as counting the solutions to a CSP (constraint satisfaction problem). The first two algorithms count all solutions to the CSP using backtrac...

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.