Graduate Program in Mathematics.Taşkın, Müge.Gümüş, Resul Bedii.2025-04-142025-04-142023Graduate Program in Mathematics. TKL 2023 U68 PhD (Thes TR 2023 L43https://digitalarchive.library.bogazici.edu.tr/handle/123456789/21626This thesis discusses the latest methods for calculating Littlewood-Richardson coefficients along with their role in the theory of group representations, symmetric functions, and Schubert varieties of Grassmanians. The methods prescribed here are constructed through honeycombs, Berenstein Zelevinky triangles, and hives. The classical approach, which uses Littlewood-Richardson tableaux, is also covered briefly since it allows us to introduce a new algorithm that efficiently calculates a lower bound for non-zero Littlewood-Richardson coefficients.Combinatorial analysis.Symmetric functions.xiii, 57 leaves