2013/12/02 by Andy Hardt, Pete McNeely, Hardt, Andy +5
Chemistry · Computer Science · Mathematics · #05C30 #Advanced Combinatorial Mathematics #Advanced Graph Theory Research #Chemistry and Stereochemistry Studies #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C30
paper · pdf · doi:10.48550/arxiv.1312.0542
39 pages, 16 figures, senior comprehensive project at Carleton College
arxiv created 2013/12/02 · openalex publication_date 2013/12/02 · arxiv updated 2013/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In enumerative combinatorics, it is often a goal to enumerate both labeled and unlabeled structures of a given type. The theory of combinatorial species is a novel toolset which provides a rigorous foundation for dealing with the distinction between labeled and unlabeled structures. The cycle index series of a species encodes the labeled and unlabeled enumerative data of that species. Moreover, by using species operations, we are able to solve for the cycle index series of one species in terms of other, known cycle indices of other species. Section 3 is an exposition of species theory and Section 4 is an enumeration of point-determining bipartite graphs using this toolset. In Section 5, we extend a result about point-determining graphs to a similar result for point-determining Φ-graphs, where Φ is a class of graphs with certain properties. Finally, Appendix A is an expository on species computation using the software Sage [9] and Appendix B uses Sage to calculate the cycle index series of point-determining bipartite graphs.