# Analysis of Bidirectional Ballot Sequences and Random Walks Ending in Their Maximum

@article{Hackl2015AnalysisOB, title={Analysis of Bidirectional Ballot Sequences and Random Walks Ending in Their Maximum}, author={Benjamin Hackl and Clemens Heuberger and H. Prodinger and Stephan G. Wagner}, journal={Annals of Combinatorics}, year={2015}, volume={20}, pages={775-797} }

Consider non-negative lattice paths ending at their maximum height, which will be called admissible paths. We show that the probability for a lattice path to be admissible is related to the Chebyshev polynomials of the first or second kind, depending on whether the lattice path is defined with a reflective barrier or not. Parameters like the number of admissible paths with given length or the expected height are analyzed asymptotically. Additionally, we use a bijection between admissible random…

## 7 Citations

The Bidirectional Ballot Polytope

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The LU-decomposition of Lehmer's tridiagonal matrix is first guessed, then proved, which leads to an evaluation of the determinant.

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