Combinatorial Interpretations and Convolutions of Catalan Numbers
| dc.contributor.advisor | Getu, Seyom (PhD) | |
| dc.contributor.author | Teka, Kibru | |
| dc.date.accessioned | 2020-12-10T07:32:00Z | |
| dc.date.accessioned | 2023-11-04T12:31:00Z | |
| dc.date.available | 2020-12-10T07:32:00Z | |
| dc.date.available | 2023-11-04T12:31:00Z | |
| dc.date.issued | 2012-01-01 | |
| dc.description.abstract | I introduced more of the combinatorial interpretations of Catalan numbers using different techniques ( interpretations) like enumeration of lattice path, ordered trees, binary trees ,etc their one to one correspondence using different theorems lemmas and rules and also an interpretations of k-th fold self convolutions of Catalan numbers by showing that they count the number of words in a symbol X and Y. Where the total number of Ys is k more than the total numbers of Xs and at no time are there more Ys than K plus the number of X’s using this we exhibit some of the wide Varity of combinatorial interpretations of self convolutions of Catalan numbers. we give anew proof of Kth- fold convolution of Catalan numbers. This is done by enumerating a certain class of polygon dissections called k in n dissections. Finally I show how these number appear as the last column in a truncated Pascal triangles. | en_US |
| dc.identifier.uri | http://etd.aau.edu.et/handle/123456789/23945 | |
| dc.language.iso | en | en_US |
| dc.publisher | Addis Ababa University | en_US |
| dc.subject | Combinatorial | en_US |
| dc.subject | Interpretations | en_US |
| dc.subject | Convolutions | en_US |
| dc.subject | Catalan Numbers | en_US |
| dc.title | Combinatorial Interpretations and Convolutions of Catalan Numbers | en_US |
| dc.type | Thesis | en_US |