Our seminar views algebraic combinatorics broadly, explicitly including algebraic enumeration and related asymptotic and bijective combinatorics, as well as algebraic combinatorics as it appears in pure algebra and in applications outside mathematics.
Our local audience consists principally of combinatorics faculty and grad students. Talks are 50 minutes with 10 minutes for questions.
Organizer: Olya Mandelshtam
Time:Thursday afternoons Waterloo time at 1pm (unless otherwise noted)
Location: The seminar will be conducted in MC 5479 and streamed over Zoom.
If you would like to attend virtually, please email Olya for the Zoom link and/or to be added to the weekly mailing list.
Fall 2022
| Date |
Speaker |
Title |
| September 15 | Jianping Pan (North Carolina State University) | A bijection between K-Kohnert diagrams and reverse set-valued tableaux
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Lascoux polynomials are K-theoretic analogues of the key polynomials. They both have combinatorial formulas involving tableaux: reverse set-valued tableaux (RSVT) rule for Lascoux polynomials and reverse semistandard Young tableaux (RSSYT) rule for key polynomials. Besides, key polynomials have a simple algorithmic model in terms of Kohnert diagrams, which are in bijection with RSSYT. Ross and Yong introduced K-Kohnert diagrams, which are analogues of Kohnert diagrams. Ross and Yong conjectured a K-Kohnert diagram rule for Lascoux polynomials. We establish this conjecture by constructing a weight-preserving bijection between RSVT and K-Kohnert diagrams.
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| September 22 | Logan Crew (Waterloo) | A graph-theoretic approach to plethysms of symmetric functions |
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Abstract: The plethysm operation f[g] of two symmetric functions is of foundational interest in algebraic combinatorics. On the representation theoretic side, it corresponds to the composition of symmetric group class functions under the Frobenius characteristic. On the symmetric function side, plethysms occur frequently as one of the most natural ways to describe operators and mappings in the space of symmetric functions.
In this talk, I will give an overview of the fundamentals of plethysm, and give a new combinatorial interpretation for any plethysm by interpreting it in terms of a signed sum over proper colorings of acyclically oriented graphs. I will demonstrate that this graph-theoretic interpretation unifies previous results and gives rise to new plethystic identities.
This is based on joint work with Sophie Spirkl.
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| September 29 | social hour! |
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| October 6 | Jean-Philippe Labbé (Université du Québec) | TBA
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| October 13 | Joel Lewis (George Washington University) | TBA
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| October 20 | Sheila Sundaram | TBA
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| October 27 | Anna Pun (CUNY-Baruch College) | TBA
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| November 3 | Jeremy Chizewer (Waterloo) | TBA
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| November 10 | Theo Douvroupolous (University of Massachusetts at Amherst) | TBA
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| November 17 | Josip Smolcic (Waterloo) | TBA
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| November 24 | --- | reading week: no seminar
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| December 1 | Sergey Yurkevich (University Paris-Saclay) |
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| December 8 | UG talks |
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Past semesters:
Spring 2022
Winter 2022
Fall 2021
Winter 2021