{"id":17000,"date":"2026-08-11T13:40:33","date_gmt":"2026-08-11T18:40:33","guid":{"rendered":"https:\/\/uwm.edu\/math\/?post_type=tribe_events&p=17000"},"modified":"2026-08-11T13:40:33","modified_gmt":"2026-08-11T18:40:33","slug":"ms-thesis-defense-menalu-mekcha","status":"publish","type":"tribe_events","link":"https:\/\/uwm.edu\/math\/event\/ms-thesis-defense-menalu-mekcha\/","title":{"rendered":"MS Thesis Defense: Menalu Mekcha"},"content":{"rendered":"

On the Combinatorics of Restricted Skew Dyck Paths<\/h2>\n

Menalu Mekcha<\/strong>
\nGraduate Student<\/strong>
\nUniversity of Wisconsin-Milwaukee<\/strong><\/p>\n

\n
This 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\u2019s decorated path framework and the kernel method to obtain level-by-level generating functions and a structural bijection explaining the level recurrence.<\/div>\n
<\/div>\n
The 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.<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

On the Combinatorics of Restricted Skew Dyck Paths Menalu Mekcha Graduate Student University of Wisconsin-Milwaukee This 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 …<\/p>\n","protected":false},"author":30596,"featured_media":0,"template":"","meta":{"_acf_changed":false,"_tribe_events_status":"","_tribe_events_status_reason":"","_tribe_events_is_hybrid":"","_tribe_events_is_virtual":"","_tribe_events_virtual_video_source":"","_tribe_events_virtual_embed_video":"","_tribe_events_virtual_linked_button_text":"","_tribe_events_virtual_linked_button":"","_tribe_events_virtual_show_embed_at":"","_tribe_events_virtual_show_embed_to":[],"_tribe_events_virtual_show_on_event":"","_tribe_events_virtual_show_on_views":"","_tribe_events_virtual_url":"","footnotes":"","uwm_wg_additional_authors":[]},"tags":[],"tribe_events_cat":[64],"class_list":["post-17000","tribe_events","type-tribe_events","status-publish","hentry","tribe_events_cat-graduate-student-defenses","cat_graduate-student-defenses"],"uwm_unpublish_requested":false,"yoast_head":"\nMathematical Sciences<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/uwm.edu\/math\/event\/ms-thesis-defense-menalu-mekcha\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"MS Thesis Defense: Menalu Mekcha\" \/>\n<meta property=\"og:description\" content=\"On the Combinatorics of Restricted Skew Dyck Paths Menalu Mekcha Graduate Student University of Wisconsin-Milwaukee This thesis studies the enumerative combinatorics of skew and restricted Dyck path families. 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