On the Mfobius Function of Pointed Partitions and Exponential Pointed Structures
| dc.contributor.advisor | Zeleke, Melkamu(Professor) | |
| dc.contributor.author | Asefa, Samuel | |
| dc.date.accessioned | 2018-07-17T13:18:56Z | |
| dc.date.accessioned | 2023-11-04T12:30:34Z | |
| dc.date.available | 2018-07-17T13:18:56Z | |
| dc.date.available | 2023-11-04T12:30:34Z | |
| dc.date.issued | 2015-05-14 | |
| dc.description.abstract | This thesis is concerned with partial orders on set and integer partitions and related structures. The study of set and integer partitions dates back to Euler and Sylvester [28]. Over the course of time it has become apparent that the combinatorics of partitions encodes important mathematical structures in a variety of felds. Results on partially ordered sets of partitions involving Mfobius numbers, homology and homotopy of order complexes emerged in the works of Rota and Stanley [56]. In this work, we use pointed partition structures where a part of an integer and set partition is marked. These have been introduced in the works of Ehrenborg and Readdy [60], Ehrenborg and Jung [63] and Ziegler [29]. We exhibit new enumerative and geometric properties of the partial orders of pointed partitions studied by Ehrenborg and Readdy [60]. In particular, we compute the Mfobius numbers and homotopy types of lower intervals. In addition, we investigate their ordered counterparts and provide analogous results in this setting. Then we use the pointed set partition lattice to introduce exponential pointed structures which are the pointed analog of exponential structures introduced by Stanley [55]. We show that this concept encompasses many examples introduced before. In particular, we introduce pointed decompositions of lattices and study their enumerative and geometric structure. We also show that exponential pointed structures satisfy pointed analogs of Stanley's compositional and exponential formulas | en_US |
| dc.identifier.uri | http://etd.aau.edu.et/handle/123456789/9066 | |
| dc.language.iso | en | en_US |
| dc.publisher | Addis Ababa University | en_US |
| dc.subject | On the Mfobius Function of Pointed Partitions | en_US |
| dc.title | On the Mfobius Function of Pointed Partitions and Exponential Pointed Structures | en_US |
| dc.type | Thesis | en_US |