Nadia Lafrenière

My research area is algebraic combinatorics. More specifically, I study actions on combinatorial structures, mostly permutations. On the one hand, I study spectral properties (eigenvalues, eigenvectors) of random walks corresponding to card shuffling which I explain in the following excerpts from national media (in French):

• In a video for the show Électrons Libres, on Télé-Québec (the video might not be available anymore)

• For the mathematics magazine Accromath

Recently, I also got interested into dynamical algebraic combinatorics, which is the study of combinatorial actions and their orbits from an enumerative perspective. I also worked in combinatorics on words in the past.

Preprints

• Ashleigh Adams, Jennifer Elder, Nadia Lafrenière, Erin McNicholas, Jessica Striker, Amanda Welch. Cyclic sieving on permutations – an analysis of maps and statistics in the FindStat database.

Published papers

• Will Dowling, Nadia Lafrenière. Homomesy on permutations with toggling actions. To appear in Involve.
• Nadia Lafrenière, Yan Zhuang. On the rix statistic and valley-hopping. Discrete Mathematics and Theoretical Computer Science, vol. 26:2, no. 3, 2024, 27 p.
• Darij Grinberg, Nadia Lafrenière. The one-sided cycle shuffles in the symmetric group algebra. Algebraic Combinatorics, Volume 7 (2024) no. 2, pp. 275-326.
• Isabelle Baraquin, Nadia Lafrenière, Katharina Schuh. The cutoff phenomenon in finite Markov chains. Snapshots of Modern Mathematics from Oberwolfach, no. 5, 2023.
• Jennifer Elder, Nadia Lafrenière, Erin McNicholas, Jessica Striker, Amanda Welch. Toggling, rowmotion, and homomesy on interval-closed sets. Accepted for publication in Journal of Combinatorics.
• Jennifer Elder, Nadia Lafrenière, Erin McNicholas, Jessica Striker, Amanda Welch. Homomesies on permutations – an analysis of maps and statistics in the FindStat database, Mathematics of Computations, 2023, 56 p.
• Nadia Lafrenière. Eigenvalues of symmetrized shuffling operators. FPSAC 2019, 12 pp.
• Damien Jamet, Nadia Lafrenière, Xavier Provençal. Generation of Digital Planes Using Generalized Continued-Fractions Algorithms. DGCI 2016, pp. 45-56.
• Srecko Brlek, Nadia Lafrenière, Xavier Provençal. Palindromic Complexity of Trees. DLT 2015, pp. 155-166.
• Srecko Brlek, Nadia Lafrenière. Reconstructing Words from a σ-palindromic Language. Fundamenta Informaticae, Vol. 135 no. 1-2, 2014, pp. 59-72.

Theses

My Ph.D. thesis, defended in November 2019, was about two families of shuffles, called the symmetrized shuffling operators. The focus was the eigenvalues. My advisor was Franco Saliola.

• Nadia Lafrenière. Valeurs propres des opérateurs de mélange symétrisés, Ph.D. thesis, Université du Québec à Montréal, 2019. (In French).

My master’s thesis was on combinatorics on words, and more specifically about palindromes. My advisors were Srecko Brlek and Xavier Provençal.

• Nadia Lafrenière. Complexité palindromique des mots et des arbres, M.Sc. thesis, Université du Québec à Montréal, 2016. (In French).

Selected talks

• Tricher à l’aide des mathématiques, Grandes conférences du Centre de recherches mathématiques, March 14, 2024. Video.
• Rowmotion on Interval-closed sets, Commutative Algebra meets Algebraic Combinatorics (CAAC), Januar 26, 2024. Slides.
• How many times should you shuffle a deck or cards?, Graduate Online Combinatorics Colloquium (invited as an expert; virtual), April 19, 2023. Notes
• Homomesy on permutations, given several times as seminar talks, and at the Joint Mathematics Meetings, January 6, 2023.
• The spectrum of the random-to-below Markov chain, given several times as seminar talks, and at the American Mathematical Society Sectional Meeting in Amherst (MA), October 2, 2022.
• Eigenvalues of symmetrized shuffling operators, Formal Power Series and Algebraic Combinatorics (FPSAC), Ljubljana, July 1st, 2019. Slides.
• Palindromic complexity of trees, Developments in Language Theory 2015, Liverpool, July 30th, 2015.