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SUMMARY:MS Thesis Defense: Menalu Mekcha
DESCRIPTION:On the Combinatorics of Restricted Skew Dyck Paths\nMenalu Mekcha\nGraduate Student\nUniversity of Wisconsin-Milwaukee \n\nThis thesis studies the enumerative combinatorics of skew and restricted Dyck path families. Beginning with classical Dyck paths\, non-decreasing Dyck paths\, and domino tilings\, we review their connections to Catalan numbers and odd-indexed Fibonacci numbers. For partial skew Dyck paths\, we use Prodinger’s decorated path framework and the kernel method to obtain level-by-level generating functions and a structural bijection explaining the level recurrence.\n\nThe main contribution concerns restricted skew Dyck paths whose valley heights form a non-decreasing sequence. By tracking semi-length and peak count\, we derive the bivariate generating function S_UD(x\,y)=xy(1-2x)/((1-2x)^2-xy(1-x)). Setting y=1 recovers the total enumeration as a Fibonacci binomial sum. Finally\, extracting row polynomials from this generating function shows that the double-indexed array s_UD(n\,m) gives a combinatorial realization of OEIS triangle A114164.
URL:https://uwm.edu/math/event/ms-thesis-defense-menalu-mekcha/
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