Question: What do the Fourier uncertainty principle, Stirling numbers, and the EE Quals have in common?
Answer: Falling factorials.
We investigate the coefficients generated by expressing the falling factorial as a linear combination of falling factorial products . Algebraic and combinatorial properties of these coefficients are discussed, in relation to Stirling numbers, binomial coefficients, and generating functions for conjoint ranking tables.
- Wu, William; Osgood, Brad. Falling Factorials, Generating Functions, and Conjoint Ranking Tables. Journal of Integer Sequences, Vol. 12 (2009), Article 09.7.8.