Counting interesting elections
Lara K. Pudwell, Eric S. Rowland
TL;DR
This paper presents a simple proof for a formula counting northeast lattice paths within a specific region, which also enumerates lattice points inside the Pitman--Stanley polytope of an n-tuple.
Contribution
It offers an elementary proof of a known formula, simplifying the understanding of lattice path enumeration and polytope point counting.
Findings
Elementary proof of the lattice path counting formula
Connection between lattice paths and Pitman--Stanley polytope
Simplification of previous combinatorial enumeration methods
Abstract
We provide an elementary proof of a formula for the number of northeast lattice paths that lie in a certain region of the plane. Equivalently, this formula counts the lattice points inside the Pitman--Stanley polytope of an n-tuple.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Markov Chains and Monte Carlo Methods