Disturbing the Dyson Conjecture (in a GOOD Way)

Presenters/Authors

Andrew V. Sills, Georgia Southern UniversityFollow

Document Type

Presentation

Presentation Date

1-5-2007

Abstract or Description

In 1962, Freeman Dyson conjectured that the constant term in the Laurent polynomial ∏_{1≤i≠j≤n}(1 − x_i/x_j )^a_j (let us call this the “Dyson product”) is the multinomial coefficient (a₁+a₂+···+a_n)!/a₁!a₂!···a_n! . Dyson’s conjecture was first proved independently by Gunson and Wilson. The most compact and elegant proof, however, was supplied by I.J. Good in 1970. We present a case study in experimental (yet rigorous!) mathematics by describing an algorithm which automatically conjectures, and then supplies proofs (inspired by Good’s proof) of closed form expressions for extensions of Dyson’s conjecture to coefficients beside the constant term in the Dyson product.

Sponsorship/Conference/Institution

Joint American Mathematical Society (AMS) and Mathematical Association of America (MAA) Meetings

Location

New Orleans, LA

Recommended Citation

Sills, Andrew V.. 2007. "Disturbing the Dyson Conjecture (in a GOOD Way)." Department of Mathematical Sciences Faculty Presentations. Presentation 407.
https://digitalcommons.georgiasouthern.edu/math-sci-facpres/407