13 citations · 16 across the 2 of their papers we have counts for
11 papers
Spanning tree size in Random Binary Search Trees
Alois Panholzer, Helmut Prodinger
This paper deals with the size of the spanning tree of p randomly chosen nodes in a binary search tree. It is shown via generating functions methods, that for fixed p, the (normali…
q-identities of Fu and Lascoux proved by the q-Rice formula
Helmut Prodinger
Two recent --identities of Fu and Lascoux are proved by the --Rice formula.
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.
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.
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…
Combinatorics of geometrically distributed random variables: New q-tangent and q-secant numbers
Helmut Prodinger
Up-down permutations are counted by tangent resp. secant numbers. Considering words instead, where the letters are produced by independent geometric distributions, there are severa…