ICE-TCS seminar: Jay Pantone
Experimental Methods in Combinatorics
ICE-TCS seminar #334
Date and time: Tuesday, 14 May 2019, 12:10-13:00
Location: Room M1.22
Speaker: Jay Pantone (Marquette University, USA)
Title: Experimental Methods in Combinatorics
Abstract: Enumerative combinatorics is the study of the structure of families of mathematical objects. Such families are ubiquitous in math and the sciences and include computer networks with connectivity restrictions, strands of RNA subject to folding constraints, and software fault-detection schemes. Often, the central question is "How many objects are there of a given size?" Many of these problems belong to families for which it is known to be difficult if not impossible to find a general formula for the number of objects of a certain size. However, with the rise of computational capabilities over the last few decades, it has become increasingly common to be able to compute the number of objects up to a certain large size.
In this case, one seeks to use the computed initial information to experimentally approximate the long-term behavior of the counting sequence. We'll discuss two such experimental methods---differential approximation and automated fitting---and show several examples of their application to open questions in enumerative combinatorics.
