Browsing by Author "Asefa, Samuel (PhD)"

Now showing 1 - 4 of 4
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    Parking Functions and Complete Bipartite Graphs
    (Addis Ababa University, 2020-11-26) Suleiman, Medina; Asefa, Samuel (PhD)
    A Parking function is a sequence of positive integers (a1; a2; : : : ; an) such that its non-decreasing rearrangement (b1; b2; : : : ; bn), satis es bi i, for all index i. In this thesis we will see about parking functions and their interrelation with other combinatorial objects; namely non-crossing partitions and labelled trees. We also discuss on the generalization of parking functions namely; G- parking functions and establish a new relationship between parking functions and spanning trees of complete bipartite graphs.
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    Shellability of Pointed Integer Partition
    (Addis Ababa University, 6/1/2018) Abebe, Ayichew; Asefa, Samuel (PhD)
    In 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.
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    Shellability of Pointed Integer Partition
    (Addis Ababa University, 2018-06-01) Abebe, Ayichew; Asefa, Samuel (PhD)
    In 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.
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    Young Tableaux and the Representations of the Symmetric Group
    (Addis Ababa University, 2021-08-25) Belete, Blen; Asefa, Samuel (PhD)
    In this work, we look at the connection between Young tableaux and sym- metric group representations. The design of Specht is discussed in detail. Two noteworthy ndings presented and followed by instances are modules that are irreducible representations of Sn, as well as many of the branching rule and Young's rule.