Date of Submission

Spring 2012

Academic Program

Computer Science; Mathematics

Project Advisor 1

Robert McGrail

Project Advisor 2

James Belk

Abstract/Artist's Statement

This senior project focuses on a collection of algebras that arise in knot theory called quandles. In particular, we study how to distinguish non-isomorphic quandles using different computational methods. Most of this work is built on The Library for Automated Deduction Research (LADR). Within LADR, the program isofilter removes the isomorphic duplicates for a collection of first-order models, but it works very slowly in general. In this senior project, we propose an augmented algorithm to filter quandles using computable invariants: we separate a stream of input quandles into different buckets based on the invariants; then we apply isofilter to the buckets containing more than one quandles. In fact, our invariant checking can distinguish most of the isomorphism classes for quandles up to size 30. It thus improves the quandle filtering process by largely reducing the use of isofilter.

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