Some q-analogs of congruences for central binomial sums
We establish q-analogs for four congruences involving central binomial coefficients. The q-identities necessary for this purpose are shown via the q-WZ method.
On fixed points of holomorphic maps of simply connected proper domains in
A criterion for the existence of fixed point of one-dimensional holomorphic maps is established.
On fixed points of extensions of expanding maps in the unit disc
Using a result due to M. Shub, a theorem about the existence of fixed points inside the unit disc for extensions of expanding maps defined on the boundary is established. An application to a special class of rational maps on the Riemann sphere and some considerations on ergodic properties of these maps are also made.
Supercongruences for the Almkvist-Zudilin numbers
We prove a conjecture on supercongruences for sequences that have come to be known as the Almkvist-Zudilin numbers. Some other (naturally) related family of sequences will be considered in a similar vain.
A common fixed point theorem for commuting expanding maps on nilmanifolds.
The dinner table problem: the rectangular case.
Congruences involving alternating multiple harmonic sums.
Edge cover time for regular graphs.
A new domino tiling sequence.
Congruences of multiple sums involving sequences invariant under the binomial transform.
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