The use of generating function and cyclotomic polynomials to discover and prove some new restricted integer partitions - Songvilay, Sonexay; Saybounheaung, Thongsouk; Namkhaluck, Innavanh; Thanavanh, Pinkham; Siharath, Phuangmaly; Vongbounsy, Parnthong; Sengthavideth, Sonephanom (Souphanouvong University Journal Multidisciplinary Research and Development, 2022)
The purposes of this research were to discovered some new partition identities valid for all positive integers of the general type where is the number of partitions of and the parts of are subject to a first restriction and is the number of partitions of and the parts of are subject to the second restriction, which is different from the first one. These partition identities are proved by using the generating function and properties of cyclotomic polynomials.