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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/
LOCATION:EMS Building\, E495\, 3200 N Cramer St\, Milwaukee\, WI\, United States
CATEGORIES:Graduate Student Defenses
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DTSTART;TZID=America/Chicago:20260819T093000
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DTSTAMP:20260811T163542Z
CREATED:20260804T175724Z
LAST-MODIFIED:20260811T163542Z
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SUMMARY:Department of Mathematical Sciences Graduate Program Orientation & Welcome Lunch
DESCRIPTION:Presented by Prof. Jeb Willenbring and Dr. Rebecca Bourn\, required for all new Graduate Students.
URL:https://uwm.edu/math/event/department-of-mathematical-sciences-graduate-program-orientation-welcome-lunch/
LOCATION:EMS Building\, E495\, 3200 N Cramer St\, Milwaukee\, WI\, United States
CATEGORIES:Fall Orientation
ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu
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DTSTART;TZID=America/Chicago:20260825T120000
DTEND;TZID=America/Chicago:20260825T143000
DTSTAMP:20260804T184110Z
CREATED:20260804T184110Z
LAST-MODIFIED:20260804T184110Z
UID:10016301-1787659200-1787668200@uwm.edu
SUMMARY:All Lecturers Meeting & Lunch
DESCRIPTION: Presented by Prof Chris Hruska\, Chair.
URL:https://uwm.edu/math/event/all-lecturers-meeting-lunch/
LOCATION:EMS Building\, E495\, 3200 N Cramer St\, Milwaukee\, WI\, United States
CATEGORIES:Fall Orientation
ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu
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