# Mathematics Wiskunde

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Friday 15 November 2019

# On a generalisation of $$k$$-Dyck paths

Speaker: Miss Sarah Selkirk
Time: 11:00
Venue: Mathematics, Room 1006

We consider a family of non-negative lattice paths consisting of the step set $$\{(1, 1), (1, -k)\}$$ called $$k$$-Dyck paths, which are enumerated by the generalised Catalan numbers. By removing the non-negativity condition but restricting the path to above the line $$y = -t$$ we obtain a family of lattice paths called $$k_t$$-Dyck paths which have interesting enumerative properties. We enumerate these paths using various combinatorial methods, and perform analysis of associated parameters.