Yi-Lin Lee
Welcome to my website. I am a 6th year mathematics Ph.D. candidate at the Indiana University Bloomington. My advisor is Mihai Ciucu.
I was a research assistant in the Institute of Mathematics, Academia Sinica and the National Center for Theoretical Science in Taiwan, under the supervision of Shun-Jen Cheng. Before that, I was an undergraduate student at the National Central University in Taiwan.
Here is my CV.
I can be reached at yillee[at]iu[dot]edu.
My research interests are in algebraic and enumerative combinatorics - in particular tilings, symmetry classes of combinatorial objects, lattice path enumeration, symmetric functions, tableaux combinatorics. I am currently working on:
more applications to the Lindström-Gessel-Viennot theorem.
symmetry classes of domino/lozenge tilings of a certain region.
extended promotion sorting.
connections between domino/lozenge tilings and symmetric polynomials.
Publications and Preprints
Off-diagonally symmetric domino tilings of the Aztec diamond of odd order.
Off-diagonally symmetric domino tilings of the Aztec diamond.
Electron. J. Combin. 30 (2023), no. 4, Paper No. 4.20, 30 pp. arxiv.org/abs/2303.02750
An extension of the Lindström-Gessel-Viennot theorem.
Electron. J. Combin. 29 (2022), no. 2, Paper No. 2.41, 31 pp. arxiv.org/abs/2112.06115
Skew standard domino tableaux and partial Motzkin paths.
with Ting-Yuan Cheng, Sen-Peng Eu, Tung-Shan Fu
Ann. Comb. 21 (2017), no. 1, 43–71.
Papers in preparation
A generalization of off-diagonally symmetric lozenge tilings. In preparation.
with Seok Hyun Byun
An application of factorization theorem to nearly reflectively symmetric graphs and beyond. In preparation.
with Seok Hyun Byun and Mihai Ciucu
Extended promotion sorting. In preparation.
with GRWC group members
Cyclic sieving phenomenon on positroids. In preparation.
with GRWC group members
Other writings
GRWC 2023 - proposed research problem.
An extension of the Jacobi-Trudi identity from the lattice paths viewpoint.
Contributed and Invited Talks
(scheduled) June 2024, Early-Career Conference in Combinatorics, UIUC
Apr. 2024, Workshop II: Integrability and Algebraic Combinatorics, UCLA
Title: Further exploration of off-diagonally symmetric domino tilings of the Aztec diamond (Slides)
Mar. 2024, Graduate Student Combinatorics Conference (GSCC), Carnegie Mellon University
Title: Off-diagonally symmetric domino tilings of the Aztec diamond (Slides)
Nov. 20, 2023, Algebra and Discrete Mathematics Seminar, Clemson University (Slides)
Oct. 7, 2023, AMS Fall Central Sectional Meeting, Creighton University
Title: Off-diagonally symmetric domino tilings of the Aztec diamond (Slides - 20 minutes version)
Oct. 4, 2023, Graduate Online Combinatorics Colloquium (GOCC), online
Title: An extension of the Lindström-Gessel-Viennot theorem (Slides - 50 minutes version)
Aug. 2023, Dimers: Combinatorics, Representation Theory and Physics, CUNY
Title: Off-diagonally symmetric domino tilings of the Aztec diamond (Slides - 30 minutes version)
June 7, 2023, Combinatorics Colloquium, National Taiwan Normal University
Title: Off-diagonally symmetric domino tilings of the Aztec diamond
May 31, 2023, Combinatorics Colloquium, National Taiwan Normal University
Title: An extension of the Lindström-Gessel-Viennot theorem
May 2023, Colloquium, National Cheng Kung University (in Taiwan)
Title: An extension of the Lindström-Gessel-Viennot theorem (Slides - 50 minutes version)
Apr. 2023, CombinaTexas 2023, Texas A&M University
Title: Off-diagonally symmetric domino tilings of the Aztec diamond (Slides - 20 minutes version)
Oct. 2022, 34th Midwestern Conference on Combinatorics and Combinatorial Computing, Illinois State University
Title: An extension of the Lindström-Gessel-Viennot theorem
Sept. 2022, The 5th Mostly Manitoba, Michigan and Minnesota Combinatorics Graduate Students Workshop, Iowa State University
Title: An extension of the Lindström-Gessel-Viennot theorem
Jun. 2022, Permutation Patterns 2022, Valparaiso University
Title: An extension of the Lindström-Gessel-Viennot theorem (Slides - 20 minutes version)
Dec. 2020, Combinatorics Colloquium, National Central University (in Taiwan)
Title: Combinatorial tiling theory on the Aztec diamond
Seminar Talks
Dec. 2020, Combinatorics Online Seminar, National Taiwan Normal University
Title: Symmetry classes of domino tilings of the Aztec diamond
Fall 2020, Graduate Student Algebraic Combinatorics Seminar, Indiana University
Title: The Littlewood-Richardson theorem
Title: Introduction to Schur functions
2019-2020, Graduate Student Combinatorics Seminar, Indiana University
Title: Introduction to chromatic polynomials
Title: Introduction to parking functions
Title: An introduction to Young tableaux
Jun. 2019, Seminar on Combinatorics, National Taiwan Normal University
Title: Some aspects of combinatorial tiling theory
Posters
Feb. 2024, Enumerative and Algebraic Combinatorics, University of Florida
Aug. 2023, Dimers: Combinatorics, Representation Theory and Physics, CUNY
Title: Off-diagonally symmetric domino tilings of the Aztec diamond