FORMULASI MODEL PERMUTASI SIKLIS DENGAN OBJEK MULTINOMIAL

Abstract

Penelitian ini bertujuan membangun model matematika untuk menghitung jumlah susunan objek dari permutasi siklis yang memiliki objek multinomial. Model yang dibangun dibatasi untuk permutasi siklis yang memiliki objek multinomial dengan minimal ada satu jenis objek beranggotakan tunggal. Pemodelan dilakukan berdasarkan struktur matematika dari permutasi siklis dan permutasi multinomial. Model permutasi siklis yang memiliki objek multinomial telah dirumuskan.   Pembuktian model telah dilakukan melalui validasi struktur serta validasi hasil yang dilakukan dengan cara membandingkan hasil perhitungan model dan hasil pencacahan. Teorema tentang permutasi siklis dengan objek multinomial juga telah dibangun.

Kata kunci:  pemodelan , permutasi siklis, permutasi multinomial

This study aims at constructing mathematical model to count the number of arrangement of objects form cyclical permutation that has multinomial objects. The model constructed is limited to cyclical permutation that has multinomial object in which at least one kind of object having single cardinality is contained within. Modelling is undertaken based on mathematical structure of cyclical permutation and multinomial permutation. Cyclical permutation model having multinomial object has been formulated as . The proof of the model has been undertaken by validating structure and validating the outcome which was conducted by comparing counting result of model and counting result manually. The theorem of cyclical permutation with multinomial object has also been developed.

Keywords: modelling, cyclical permutation, multinomial permutation