<p dir="ltr">We present first order asymptotic estimates for the divisor function problem, the set of lists (restricted number of divisors) problem, and a generalization of the overpartition problem. In particular, we prove Kotesovec's conjecture for A294363 from the OEIS and also extend his conjecture to a full asymptotic treatment by providing an estimate in terms of elementary functions for the EGF coefficients directly rather than the log of the coefficients. We also provide asymptotic estimates for generalizations of the set of lists and overpartition problem, while making comparisons to any existing Kotesovec conjectures. We perform the asymptotic analysis via Mellin transforms, residue analysis, and the saddle point method. These families of generating functions have potential application to families of randomly generated partitions in which ordered subsets of a partition that exceed a certain fixed size may be one of two different objects and to overpartitions with potential heading labels.</p>
| Identifer | oai:union.ndltd.org:purdue.edu/oai:figshare.com:article/26354077 |
| Date | 27 July 2024 |
| Creators | Evan Hanlei Li (19196401) |
| Source Sets | Purdue University |
| Detected Language | English |
| Type | Text, Thesis |
| Rights | CC BY 4.0 |
| Relation | https://figshare.com/articles/thesis/Analytic_Complex-Valued_Methods_for_Randomly_Generated_Structures/26354077 |
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