Department of Mathematics

Combinatorics and Graph Theory

  •  Nadia Lafrenière, Dartmouth
  •  A Study Of Homomesy On Permutations Using The FindStat Database
  •  10/26/2022
  •  3:00 PM - 3:50 PM
  •  Online (virtual meeting) (Virtual Meeting Link)
  •  Bruce E Sagan (

We performed a systematic study of permutation statistics and bijective maps on permutations, looking for the homomesy phenomenon. Homomesy occurs when the average value of a statistic is the same on each orbit of a given map. The maps that exhibit homomesy include the Lehmer code rotation, the reverse, the complement, and the Kreweras complement, all of which have some geometric interpretations. The statistics studied relate to familiar notions such as inversions, descents, and permutation patterns, among others. Beside the many new homomesy results, I’ll discuss our research method, in which we used SageMath to search the FindStat combinatorial statistics database to identify potential instances of homomesy, and what this experiment taught us about the maps themselves and the homomesy phenomenon at large. This is joint work with Jennifer Elder, Erin McNicholas, Jessica Striker and Amanda Welch.



Department of Mathematics
Michigan State University
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East Lansing, MI 48824

Phone: (517) 353-0844
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