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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.
DOI: 10.15480/882.3952
Institute: Mathematik E-10 
Document Type: Thesis
Thesis Type: Doctoral Thesis
Advisor: Taraz, Anusch 
Referee: Srivastav, Anand 
License: In Copyright In Copyright
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