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The Department of Mathematics is a bustling place full of new ideas. We host several events that occur throughout the year, including seminars, colloquium, conferences, and social events. Our seminars and colloquium are open to the public: all students, faculty, or alumni who are interested are welcome to join us for exciting talks on the leading edge of mathematics research!

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Graph Theory and Combinatorics Seminar: Ryser's Theorem for rho-Latin Rectangles

Event Type
Feb 1, 2022   1:00 pm  
Amin Bahmanian (Illinois State University)
Sean English
Let L be an n x n array whose  top left r x s subarray is filled with k different symbols, each occurring at most once in each row and at most once in each column. We find necessary and sufficient conditions that ensure the remaining cells of L can be filled such that each symbol occurs at most once in each row and at most once in each column, and each symbol occurs a prescribed number of times in L. The case where the prescribed number of times each symbol occurs is n was solved by Ryser (1951), and the case s=n was settled by Goldwasser et al. (2015). Our technique leads to a very short proof of the latter.
For Zoom information, please contact Sean at SEnglish (at) illinois (dot) edu.
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