Extending Partial Orders to Dense Linear Orders

A Ramsey theorem for partial orders with linear extensions

We prove a Ramsey theorem for finite sets equipped with a partial order and a fixed number of linear orders extending the partial order. This is a common generalization of two recent Ramsey theorems due to Sokić. As a bonus, our proof gives new arguments for these two results.

Reflecting Linear Arithmetic: From Dense Linear Orders to Presburger Arithmetic

This talk presents reflected quantifier elimination procedures for both integer and real linear arithmetic. Reflection means that the algorithms are expressed as recursive functions on recursive data types inside some logic (in our case HOL), are verified in that logic, and can then be applied to the logic itself. After a brief overview of reflection we will discuss a number of quantifier elimi...

Extending Partial Orders on O-minimal Structures to Deenable Total Orders

A Batch-wise ATP Procedure in Hybrid Make-to-Order/Make-to-Stock Manufacturing Environment

Satisfying customer demand necessitates manufacturers understanding the importance of Available-To-Promise (ATP). It directly links available resources to customer orders and has significant impact on overall performance of a supply chain. In this paper, an improvement of the batch-mode ATP function in which the partial fulfillment of the orders is available will be proposed. In other words, in...

Maximum sum element orders of all proper subgroups of PGL(2, q)

In this paper we show that if q is a power of a prime p , then the projective special linear group PSL(2, q) and the stabilizer of a point of the projective line have maximum sum element orders among all proper subgroups of projective general linear group PGL(2, q) for q odd and even respectively