Sivasubramanian, Sivaramakrishnan

Hankel determinants of some sequences of polynomials

Sémin. Lothar. Comb. 63, B63d, 8 p., electronic only (2010)


Summary: Ehrenborg gave a combinatorial proof of Radoux's theorem which states that the determinant of the $(n+1)x(n+1)$ dimensional Hankel matrix of exponential polynomials is $x^{n(n+1)/2}$ prod_i=0^n i!. This proof also shows the result that the $(n+1)x(n+1)$ Hankel matrix of factorial numbers is $\prod_{k=1}^n (k!)^{2}$. We observe that two polynomial generalizations of factorial numbers also have interesting determinant values for Hankel matrices.