Shellability Of Pointed Integer Partition

In this thesis we study, Pointed integer partition de ned as a pair fu;mg = fu1; u2; ; ur;mgrnwhere u = fu1; u2; ; urg is an integer partition of nÀ€€m, and m is a non-negative integerrn n. Shellability of pointed integer partition with M obius values -1 and +1 denotedrnby Rn. We determine the cardinality of I rnn and Rn for 1 n 10 and n 1 respectivelyrnand the Hasse diagram and the M obius values of I rnn for 1 n 6. In addition to thesernwe have determined the edge labeling of Rn for n 3 using the technique for labelingrnthe edges of the Hasse diagram of Rn, according to [12], Rn admit an EL-labeling whichrnis EL-shellable.

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