Math Colloquium: "Combinatorics of finite fields and symmetric functions"

Math Colloquium: "Combinatorics of finite fields and symmetric functions"http://www.haverford.edu/calendar/details/224111KINSC E3092012-12-10T16:00:002012-12-10T17:00:00

December 10, 4:00PM

KINSC E309

Ryan Vinroot (College of William and Mary). KINSC E309.

Description

Bi-College Mathematics Colloquium

"Combinatorics of finite fields and symmetric functions"

Ryan Vinroot, College of William and Mary.

Talk at 4:00 in KINSC E309

Tea at 3:00 in KINSC H208, the Math Lounge

Abstract:

I will begin by introducing the q-binomial coefficient, which is a q-analogue of the regular binomial coefficient, and counts subspaces in vector spaces over a field with q elements.  The q-multinomial coefficients are defined analogously, and count flags of subspaces.  I will then give some interesting recursions of sums of these quantities.  The q-binomial coefficients are then used to define the Rogers-Szego polynomials in a single variable, which have played an important role in number theory as well as the theory of orthogonal polynomials.  Multivariate Rogers-Szego polynomials are defined using q-multinomial coefficients, and these polynomials have nice recursions similar to those introduced in the beginning of the talk.  Finally, I will give a new result, obtained in joint work with undergraduate Stephen Cameron from William and Mary, which is a product formula for multivariate Rogers-Szego polynomials.  This formula has an interesting interpretation in terms of symmetric functions, and has the potential for further generalization in this direction.

Link: http://www.haverford.edu/mathematics/events/colloquium.php

For More Info

Joshua Sabloff
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