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Increasing subsequences, orbit harmonics, and shadow play

Brendon Rhoades, University of California, San Diego
Wednesday, April 3, 2024 - 3:30pm to 5:00pm
PDL C-401 and via Zoom Link:


The Schensted correspondence is a bijection between permutations in \$S_n\$ and pairs of standard Young tableaux \$(P,Q)\$ with \$n\$ boxes which have the same shape. This bijection has remarkable properties in algebraic and enumerative combinatorics. Motivated by a problem in cryptography, we study a graded quotient \$R_n\$ of the polynomial ring in \$n \times n\$ variables whose standard monomial theory encodes Viennot's shadow line formulation of the Schensted correspondence. The quotient ring \$R_n\$ may be understood as coming from the locus of permutation matrices via the machine of orbit harmonics. I will report on work of my student Moxuan Liu who has extended this theory to colored permutation groups.

Note: This talk begins with a pre-seminar (aimed at graduate students) at 3:30–4:00. The main talk starts at 4:10.

Join Zoom Meeting:
Meeting ID: 915 4733 5974