Shellability of Pointed Integer Partition
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Date
2018-06-01
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Addis Ababa University
Abstract
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 nm, 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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Keywords
Pointed Integer Partition, Hassee diagram and Shellability