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Creators/Authors contains: "Lafrenière, Nadia"

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Toggling, rowmotion, and homomesy on interval-closed sets

https://doi.org/10.4310/JOC.240906223550

Elder, Jennifer; Lafrenière, Nadia; McNicholas, Erin; Striker, Jessica; Welch, Amanda (September 2024, Journal of Combinatorics)

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Homomesies on permutations: An analysis of maps and statistics in the FindStat database

https://doi.org/10.1090/mcom/3866

Elder, Jennifer; Lafrenière, Nadia; McNicholas, Erin; Striker, Jessica; Welch, Amanda (March 2024, Mathematics of Computation)

In this paper, we perform a systematic study of permutation statistics and bijective maps on permutations in which we identify and prove 122 instances of the homomesy phenomenon. Homomesy occurs when the average value of a statistic is the same on each orbit of a given map. The maps we investigate include the Lehmer code rotation, the reverse, the complement, the Foata bijection, and the Kreweras complement. The statistics studied relate to familiar notions such as inversions, descents, and permutation patterns, and also more obscure constructs. Besides the many new homomesy results, we discuss our research method, in which we used SageMath to search the FindStat combinatorial statistics database to identify potential homomesies.
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Ian G. 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Ram, Arun; Macdonald, Ian G; Pilaud, Vincent; Poliakova, Daria; Defant, Colin; Madhukara, Rachana; Thomas, Hugh; Iraci, Alessandro; Nadeau, Philippe; Vanden_Wyngaerd, Anna; et al (September 2024, Séminaire lotharingien de combinatoire)
Gaetz, Christian (Ed.)
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