# Exact Pattern Containment in Restricted Growth Functions

## Location

King Building 341

## Document Type

Presentation

## Start Date

4-29-2016 4:00 PM

## End Date

4-29-2016 5:15 PM

## Abstract

In the mathematical field of enumerative combinatorics, we study the number of ways a pattern can emerge given certain constraints. In my research I examine the ways that a mathematical object called a “restricted growth function” (RGF) can be contained in another RGF and the distribution of certain “combinatorial statistics” on sets of RGF’s containing others. I find connections to many famous combinatorial objects such as set partitions, integer partitions, Fibonacci numbers, Pascal’s triangle, Catalan numbers, and more.

## Recommended Citation

Dorward, Robert, "Exact Pattern Containment in Restricted Growth Functions" (04/29/16). *Senior Symposium*. 14.

https://digitalcommons.oberlin.edu/seniorsymp/2016/presentations/14

## Major

Computer Science; Mathematics

## Advisor(s)

Alexa Sharp, Computer Science

Lola Thompson, Mathematics

## Project Mentor(s)

Kevin Woods, Mathematics

April 2016

Exact Pattern Containment in Restricted Growth Functions

King Building 341

In the mathematical field of enumerative combinatorics, we study the number of ways a pattern can emerge given certain constraints. In my research I examine the ways that a mathematical object called a “restricted growth function” (RGF) can be contained in another RGF and the distribution of certain “combinatorial statistics” on sets of RGF’s containing others. I find connections to many famous combinatorial objects such as set partitions, integer partitions, Fibonacci numbers, Pascal’s triangle, Catalan numbers, and more.

## Notes

Session III, Panel 16 - On Surfaces and Edges: Using Numbers to Make Sense of Sound, Time, and Patterns

Moderator: Bob Geitz, Associate Professor of Computer Science