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Hurwitz enumeration problem is an old but still active research problem due to its connections to several modern areas of mathematics and physics. Although, the formulation of the problem is purely of topological nature, interesting results comes algebraically and combinatorially. In this paper, we aim to provide an accessible exposition to various formulae for calculating Hurwitz numbers. Hurwitz numbers have a rich geometric structure behind them which has attracted many mathematicians and physicists.
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