Research

• Pattern avoidance

  • L. Cao and S.-F. Tsai, Pattern forcing (0,1)-matrices. Submitted. arXiv: 2510.27076 (2025)

  • J. Geneson and S.-F. Tsai, Extremal bounds for pattern avoidance in multidimensional 0-1 matrices. Discrete Mathematics 348 (2025) 114303

  • Anand, J. Geneson, S. Kaustav, and S.-F. Tsai, Sequence saturation. Discrete Applied Mathematics 360: 382-393 (2025)

  • S.-F. Tsai, Saturation of multidimensional 0-1 matrices. Discrete Mathematics Letter, 11:91–95, (2023)

  • J. Geneson and S.-F. Tsai, Sharper bounds and structural results for minimally nonlinear 0-1 matrices. Electronic Journal of Combinatorics 27: P4.24 (2020)

  • P.A. CrowdMath (pseudonym for J. Geneson and S.-F. Tsai), Bounds on Parameters of Minimally Nonlinear Patterns. Electronic Journal of Combinatorics 25: P1.5 (2018)

• Graph theory

  • B. Brimkov, P. Diao, J. Geneson, C. Reinhart, S.-F. Tsai, W. Wang, K. Worley, Throttling for metric dimension and its variants. Theoretical Computer Science 1073 (2026)

  • J. Geneson and S.-F. Tsai, Fault tolerance for metric dimension and its variants. Discrete Applied Mathematics 383: 339-354 (2026)

  • J. Geneson and S.-F. Tsai, Random processes for generating task-dependency graphs. Submitted. arXiv: 2305.05205 (2023)

  • J. Geneson and S.-F. Tsai, Peripherality in networks: theory and applications. Journal of Mathematical Chemistry 60: 1021-1079 (2022)

• General Discrete Mathematics

  • S.-F. Tsai, Two properties of maximal antichains in strict chain product poset. Contributions to Discrete Mathematics 15: 130-132 (2020)

  • S.-F. Tsai, A simple upper bound on the number of antichains in [t]^n. Order 36: 507-510 (2019)

• Industrial white paper

  • S.-F. Tsai, E. S. Skvortsov, J. Koehler, HLL-based TV panel audience extrapolation compatible with online audience measurement from Logs. Technical report, Google LLC (2021)

Patents

• E. S. Skvortsov, S.-F. Tsai, Systems and methods for cross media reporting by fast merging of data sources. US Patent App. 18/958,927, 2025

• Z. C. Frazier, A. Ulbrich, T. A. Vaughan, Z. Wang, S.-F. Tsai, E. Skvortsov, Reducing errors introduced by model updates. US Patent App. 16/476,410, 2021

• B.-C. Peng, S.-F. Tsai, G. Yang, Transmitter and data transmission method. US Patent App. 11/952,394, 2009

Teaching

• Introduction to Computer I, Fall 2026

• Discrete Mathematics I, Fall 2026

• Project Erdos

• Algorithm I, Spring 2026

• Introduction to Computer I, Spring 2026

• Graph theory I, Fall 2025

• Algorithm I, Spring 2025

• Graph theory I, Fall 2024

• Introduction to Computer I, Spring 2024

• Topcis in Combinatorics I, Spring 2023

Talks

• On pattern-avoiding hypermatrices and higher-dimensional partitions. Aug 27, 2026, Asiacomb, Daejeon, South Korea

• Throttling for metric dimension and its variants. Jan 21, 2026. Annual Meeting of TMS.

• Saturation of 0-1 matrices. June 26, 2025, the 26th Conference of the International Linear Algebra Society, Kaohsiung, Taiwan

• Fault tolerance for metric dimension and its variants. May 25, 2025, One-day workshop in enumerative/algebraic combinatorics, Taiwan

• April 11, 2025. 建國中學

• 01陣列的極值組合學. June 20, 2024. 新竹中學

• Random walks and effective resistance on graphs and digraphs. May 24, 2024, Department of Applied Mathematics, National Sun Yat-sen University, Taiwan

• Extremal combinatorics on pattern avoidance. April 19, 2024, Institute of Communications Engineering, National Yang Ming Chiao Tung University, Taiwan

• Extremal combinatorics on pattern avoidance. Feb 29, 2024, Department of Electrical Engineering, National Cheng Kung University, Taiwan

• Extremal bounds for pattern avoidance in 0-1 matrices. Jan 23, 2024, Annual Meeting of TMS

• Extremal bounds for pattern avoidance in 0-1 matrices. Dec 11, 2023, Department of Mathematics, National Tsing Hua University, Taiwan

• 台大電信所校友回娘家. Nov 13, 2023

• Extremal bounds for pattern avoidance in 0-1 matrices. Aug 28, 2023, New-sprout Symposium for Young Combinatorics

• Saturation of high dimensional 0-1 matrices. July 27, 2023, NCTS One-day Combinatorics Workshop

• Saturation of high dimensional 0-1 matrices. July 12, 2023, 2023 International Conference on Graph Theory and Combinatorics & Twelfth Cross-strait Conference on Graph Theory and Combinatorics

• Extremal combinatorics on pattern avoidance. May 22, 2023, Department of Mathematical Sciences, National Chengchi University, Taiwan

• 美國求學、工作、與生活經驗談。2023年2月21日，國立中山大學電機系

• 數學常數e與其應用。2022年12月25日，國立中山大學應用數學系人才培育班

• Extremal combinatorics on pattern avoidance. Nov 10, 2022, Department of Applied Mathematics, National Sun Yat-sen University, Taiwan

• Logica: a declarative query language for Big Data. Nov 1, 2022, Institute of Computational and Modeling Science, National Tsing Hua University, Taiwan