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Proof of two conjectures of Zuber on fully packed loop configurations
F. Caselli, C. Krattenthaler
Two conjectures of Zuber [``On the counting of fully packed loops configurations. Some new conjectures,'' preprint] on the enumeration of configurations in the fully packed loop mo…
Descending plane partitions and rhombus tilings of a hexagon with triangular hole
Christian Krattenthaler
It is shown that the descending plane partitions of Andrews can be geometrically realized as cyclically symmetric rhombus tilings of a certain hexagon where an equilateral triangle…
On a hypergeometric identity of Gelfand, Graev and Retakh
Christian Krattenthaler, Hjalmar Rosengren
A hypergeometric identity equating a triple sum to a single sum, originally found by Gelfand, Graev and Retakh [Russian Math. Surveys 47 (1992), 1-88] by using systems of different…
An Entry of Ramanujan on Hypergeometric Series in his Notebooks
K. Srinivasa Rao, G. Vanden Berghe, Christian Krattenthaler
Example 7, after Entry 43, in Chapter XII of the first Notebook of Srinivasa Ramanujan is proved and, more generally, a summation theorem for , where …
Equations in finite semigroups: Explicit enumeration and asymptotics of solution numbers
Christian Krattenthaler, Thomas Müller
We study the number of solutions of the general semigroup equation in one variable, $X^\al=X^\be$, as well as of the system of equations in , the wr…