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math.CO2000
The Eigenvectors of the Right-Justified Pascal Triangle: A Shorter Proof with Generating Functions
Helmut Prodinger
Instead of dealing with cumbersome binomial identities, we prove Callan's result using generating functions.
math.CO2000
Kirkman's hypothesis revisited
A. Panholzer, H. Prodinger
Watson proved Kirkman's hypothesis (partially solved by Cayley). Using Lagrange Inversion, we drastically shorten Watson's computations and generalize his results at the same time.
math.CO2000
Schur's old determinant proves a brand-new theorem of Garrett-Ismail-Stanton
Helmut Prodinger
Garrett, Ismail, and Stanton gave a general formula that contains the Rogers-Ramanjuan identities as special cases. We show how easy this is when using a determinant that Schur int…