Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 11 2 2026 06 01 Hyperbolic $k$-Mersenne and $k$-Mersenne-Lucas Quaternions with it’s associated Spinor algebra 521 537 14833 10.22049/cco.2024.29372.1966 EN Ritanjali Mohanty Department of Mathematics, Central University of Jharkhand, India Hrishikesh Mahato Department of Mathematics, Central University of Jharkhand, India Journal Article 2024 01 19 In this article, we introduce and study hyperbolic $k$-Mersenne and $k$-Mersenne-Lucas spinors. First, we give hyperbolic $k$-Mersenne and $k$-Mersenne-Lucas quaternions with some algebraic properties. Next we introduce the spinor family of $k$-Mersenne and $k$-Mersenne-Lucas numbers using the hyperbolic $k$-Mersenne and $k$-Mersenne-Lucas quaternions. Here, we start with Binet-type formulas and algebraic properties such as Catalan's identity, Cassini's identity, d'Ocagne's identity, etc. Additionally, we obtain various types of generating functions. Moreover, we give partial sum formulas in closed form. https://comb-opt.azaruniv.ac.ir/article_14833_2ffc90783d16895e4be50e77eeb1c98a.pdf