TY - JOUR AU - B. Chakraborty AU - S. Chakraborty PY - 2020/07/15 Y2 - 2024/03/28 TI - On the cardinality of unique range sets with weight one JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 72 IS - 7 SE - Research articles DO - 10.37863/umzh.v72i7.6022 UR - https://umj.imath.kiev.ua/index.php/umj/article/view/6022 AB - UDC 517.9Two meromorphic functions $f$ and $g$ are said to share the set $S\subset \mathbb{C}\cup\{\infty\}$ with weight $l\in\mathbb{N}\cup\{0\}\cup\{\infty\},$ if $E_{f}(S,l)=E_{g}(S,l),$ where $$$E_{f}(S,l)=\bigcup_{a \in S} \big \{(z,t) \in \mathbb{C}\times\mathbb{N} \bigm| f(z)=a \; \text{with multiplicity} \;p \big \},$$ where $t=p$ if $p\leq l$ and $t=p+1$ if $p>l.$In this paper, we improve and supplement the result of L. W. Liao and C. C. Yang [Indian J.  Pure and Appl.  Math., 31, No~4, 431–440 (2000)] by showing that there exist a finite set $S$ with 13 elements such that $E_{f}(S,1)=E_{g}(S,1)$ implies $f\equiv g.$ ER -