FUNGSI PEMBANGKIT DALAM PEMECAHAN MASALAH KOMBINATORIKA: SYSTEMATIC LITERATURE REVIEW

DOI: https://doi.org/10.30605/r8t0f450

Authors

  • Herlinawati Universitas Islam Negeri Syekh Ali Hasan Ahmad Addary Padangsidimpuan image/svg+xml
  • Almira Amir Universitas Islam Negeri Syekh Ali Hasan Ahmad Addary Padangsidimpuan image/svg+xml
  • Rahmat Badawi Universitas Islam Negeri Syekh Ali Hasan Ahmad Addary Padangsidimpuan image/svg+xml

Kata kunci: fungsi pembangkit, kombinatorika, matematika diskrit, enumerasi, systematic literature review.

Abstract

Fungsi pembangkit merupakan salah satu konsep penting dalam matematika diskrit yang menyediakan representasi aljabar terhadap barisan bilangan dan dapat digunakan untuk menyelesaikan berbagai persoalan kombinatorika. Penelitian ini bertujuan untuk mengkaji secara sistematis perkembangan penggunaan fungsi pembangkit dalam pemecahan masalah kombinatorika, bentuk fungsi pembangkit yang digunakan, jenis masalah yang diselesaikan, serta strategi matematis yang dominan digunakan dalam penelitian mutakhir. Penelitian menggunakan metode Systematic Literature Review (SLR) dengan pedoman Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA 2020). Literatur yang dikaji dibatasi pada publikasi tahun 2021 sampai 2026 yang membahas fungsi pembangkit dalam konteks kombinatorika, enumerasi, barisan, partisi, permutasi, lintasan, dan struktur diskrit lainnya. Analisis dilakukan melalui identifikasi, penyaringan, seleksi kelayakan, ekstraksi data, dan sintesis tematik. Hasil kajian menunjukkan bahwa fungsi pembangkit memiliki peran utama sebagai alat untuk mentransformasikan masalah enumerasi menjadi persoalan aljabar, memperoleh hubungan rekursif, mengekstraksi koefisien, serta menganalisis sifat asimtotik suatu barisan. Fungsi pembangkit biasa, fungsi pembangkit eksponensial, fungsi pembangkit multivariat, dan fungsi pembangkit rasional merupakan bentuk yang paling relevan dalam pemecahan masalah kombinatorika. Kajian juga menunjukkan bahwa fungsi pembangkit tidak hanya berperan sebagai teknik perhitungan, tetapi sebagai kerangka representasi yang menghubungkan struktur kombinatorial dengan manipulasi aljabar dan analisis koefisien. Temuan ini menunjukkan peluang pengembangan penelitian pada integrasi fungsi pembangkit dengan metode komputasional, kombinatorika analitik, dan pembelajaran matematika diskrit.

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Published

2026-09-22

Issue

Vol. 11 No. 3 (2026): Pedagogy : Jurnal Pendidikan Matematika

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Copyright (c) 2026 Rahmat Badawi, Herlinawati, Almira Amir

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How to Cite

FUNGSI PEMBANGKIT DALAM PEMECAHAN MASALAH KOMBINATORIKA: SYSTEMATIC LITERATURE REVIEW. (2026). Pedagogy: Jurnal Pendidikan Matematika, 11(3), 546-559. https://doi.org/10.30605/r8t0f450