preprint · arXiv (Cornell University) · 2013

Combinatorial species and graph enumeration

Andy Hardt, Pete McNeely, Tung Phan, Justin M. Troyka

Cited by 2Open access

Abstract

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.

Cite this paper

APA 7

Hardt, A., McNeely, P., Phan, T., & Troyka, J. M. (2013). Combinatorial species and graph enumeration. arXiv (Cornell University). https://doi.org/10.48550/arxiv.1312.0542

MLA 9

Hardt, Andy, et al. “Combinatorial species and graph enumeration.” arXiv (Cornell University), 2013, https://doi.org/10.48550/arxiv.1312.0542.

Chicago

Hardt, Andy, Pete McNeely, Tung Phan, and Justin M. Troyka. 2013. “Combinatorial species and graph enumeration.” arXiv (Cornell University). https://doi.org/10.48550/arxiv.1312.0542.

Harvard

Hardt, A. et al. (2013) ‘Combinatorial species and graph enumeration’, arXiv (Cornell University). Available at: https://doi.org/10.48550/arxiv.1312.0542.

BibTeX

@misc{hardt2013combinatorial,
  title = {{Combinatorial species and graph enumeration}},
  author = {Hardt, Andy and McNeely, Pete and Phan, Tung and Troyka, Justin M.},
  journal = {arXiv (Cornell University)},
  year = {2013},
  doi = {10.48550/arxiv.1312.0542}
}

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