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https://doi.org/10.15480/882.3952

Title: | New combinatorial proofs for enumeration problems and random anchored structures | Language: | English | Authors: | Haupt, Alexander ![]() |
Keywords: | combinatorial proofs; bijective proofs; selbergs integral formula; domino towers; rook paths; anchored random structures | Issue Date: | 2021 | Examination Date: | 21-Sep-2021 | Source: | Technische Universität Hamburg (2021) | Abstract (german): | Wir finden einen kombinatorischen Beweis der Selbergschen Integralformel, welches eine Frage von Stanley beantwortet. Dann zählen wir S-omino-Türme bijektiv ab. Auch berechnen wir die erzeugende Funktion von reihenkonvexen k-omino-Türmen. Anschließend zählen wir Rundwege auf einem Schachbrett, die ein Turm ablaufen kann, bijektiv ab. Zuletzt beschäftigen wir uns mit einer probabilistischen Version eines kombinatorischen Problems von Freedman. |
Abstract (english): | This thesis is divided into four parts. We present a combinatorial proof of Selberg's integral formula, which answers a question posed by Stanley. In the second part we enumerate S-omino towers bijectively. We also calculate the generating function of row-convex k-omino towers. In the third part we enumerate walks a rook can move along on a chess board. Finally, we study a new probabilistic version of a combinatorial problem posed by Freedman. |
URI: | http://hdl.handle.net/11420/11138 | DOI: | 10.15480/882.3952 | Institute: | Mathematik E-10 | Document Type: | Thesis | Thesis Type: | Doctoral Thesis | Advisor: | Taraz, Anusch | Referee: | Srivastav, Anand | License: | ![]() |
Appears in Collections: | Publications with fulltext |
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