Welcome to my website. I am a postdoc in the research group of Sen-Peng Eu at National Taiwan Normal University.
I graduated from Indiana University in 2025 with a PhD in Mathematics. My advisor was Mihai Ciucu. Before that, 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. 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. yillee@ntnu.edu.tw
My research interests are in algebraic, dynamical, and enumerative combinatorics. Currently, I am establishing connections between tilings and symmetric polynomials and developing techniques for enumerating weighted tilings. Additionally, I am studying the structure of combinatorial objects under a group action or an operator. I am also interested in combinatorial models that arise from representation theory and statistical mechanics. I am working on:
more applications to the Lindström-Gessel-Viennot theorem.
symmetry classes of domino/lozenge tilings of a certain region.
extended promotion operator.
connections between domino/lozenge tilings and symmetric polynomials.
Publications and Preprints
8. Block diagonally symmetric lozenge tilings. Submitted.
with Seok Hyun Byun
7. Domino Tilings, Domino Shuffling, and the Nabla Operator. Submitted.
with Ian Cavey
6. Promotion, Tangled Labelings, and Sorting Generating Functions. Submitted.
with Margaret Bayer, Herman Chau, Mark Denker, Owen Goff, Jamie Kimble, and Jinting Liang
5. Propp’s benzels and Lai’s nearly symmetric hexagons with holes. Accepted.
with Seok Hyun Byun and Mihai Ciucu
4. Off-diagonally symmetric domino tilings of the Aztec diamond of odd order.
Adv. in Appl. Math. 161 (2024), Paper No. 102759, 35 pp. arxiv.org/abs/2404.09057
3. 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
2. 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
1. Skew standard domino tableaux and partial Motzkin paths.
with Ting-Yuan Cheng, Sen-Peng Eu, and Tung-Shan Fu
Ann. Comb. 21 (2017), no. 1, 43–71.
Peer-reviewed conference proceedings
Domino Tilings and Macdonald Polynomials. Contributed poster
With Ian Cavey.
Séminaire Lotharingien Combinatoire 93B (2025), Article #80.
Proceedings of the 37th Conference on Formal Power Series and Algebraic Combinatorics, Hokkaido, Japan
Other writings
GRWC 2023 - proposed research problem.
An extension of the Jacobi-Trudi identity from the lattice paths viewpoint.
Contributed and Invited Talks
Jan. 2026 (scheduled), TMS Annual Meeting (special session on discrete mathematics), National Chung Cheng University (中正大學)
Nov. 27, 2025 (scheduled), Colloquium, National Central University (中央大學)
Nov. 20, 2025 (scheduled), Colloquium, National Kaohsiung Normal University (高雄師範大學)
Oct. 22, 2025 (Scheduled), Colloquium, National University of Kaohsiung (高雄大學)
Aug. 2025, New-sprout Symposium for Young Combinatorists, Fu Jen Catholic University (輔仁大學) (Slides)
June 2025, The 26th Conference of the International Linear Algebra Society, National Sun Yat-sen University (中山大學) (Slides)
Mar. 2025, AMS Spring Southeastern Sectional Meeting, Clemson University (Slides)
Jan. 30, 2025, Algebra-Geometry-Combinatorics Seminar, UIUC (Slides)
June 2024, Early-Career Conference in Combinatorics, UIUC (Slides)
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 (臺灣師範大學)
Title: Off-diagonally symmetric domino tilings of the Aztec diamond
May 31, 2023, Combinatorics Colloquium, National Taiwan Normal University (臺灣師範大學)
Title: An extension of the Lindström-Gessel-Viennot theorem
May 2023, Colloquium, National Cheng Kung University (成功大學)
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 (中央大學)
Title: Combinatorial tiling theory on the Aztec diamond
Posters
Jul. 2025, FPSAC 2025, Hokkaido University
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
Seminar Talks
Fall 2025, Combinatorics Seminar, National Taiwan Normal University
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: An introduction to Schur functions
2019-2020, Graduate Student Combinatorics Seminar, Indiana University
Title: An introduction to chromatic polynomials
Title: An 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