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  • A Chinese Remainder Theorem for Partitions 
    KAYANATTATH, SEETHALAKSHMI (2019-04)
    Given natural numbers s, t such that gcd(s, t) = d, lcm(s, t) = m, an s-core σ, and a t-core τ , we write N_{σ, τ}(k) for the number of m-cores of length no greater than k whose s-core is σ and t-core is τ. In this thesis, ...
  • Counting Cores and Bar Cores: From Modular Forms to McKay numbers 
    KHANNA, ADITYA (2022-05)
    In this thesis, we delve into the theory of cores of partitions and tackle two main problems: the enumeration of t-cores and t-bar cores, and the computation of McKay numbers for the symmetric and alternating groups. For ...