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New combinatorial proofs for enumeration problems and random anchored structures
Citation Link: https://doi.org/10.15480/882.3952
Publikationstyp
Thesis
Thesis Type
Doctoral Thesis
Publikationsdatum
2021
Sprache
English
Author
Advisor
Referee
Title Granting Institution
Technische Universität Hamburg
Place of Title Granting Institution
Hamburg
Examination Date
2021-09-21
Institut
Citation
Technische Universität Hamburg (2021)
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.
Schlagworte
combinatorial proofs
bijective proofs
selbergs integral formula
domino towers
rook paths
anchored random structures
DDC Class
500: Naturwissenschaften
510: Mathematik