Asefa, Samuel (PhD)Abebe, Ayichew2019-04-112023-11-292019-04-112023-11-292018-06-01http://etd.aau.edu.et/handle/123456789/17837In this thesis we study, Pointed integer partition de ned as a pair fu;mg = fu1; u2; ; ur;mg where u = fu1; u2; ; urg is an integer partition of n􀀀m, and m is a non-negative integer n. Shellability of pointed integer partition with M obius values -1 and +1 denoted by Rn. We determine the cardinality of I n and Rn for 1 n 10 and n 1 respectively and the Hasse diagram and the M obius values of I n for 1 n 6. In addition to these we have determined the edge labeling of Rn for n 3 using the technique for labeling the edges of the Hasse diagram of Rn, according to [12], Rn admit an EL-labeling which is EL-shellable.enPointed Integer PartitionHassee diagram and ShellabilityThesis