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math.NT2025
Distribution of the sum of reciprocal parts for distinct parts partitions
Walter Bridges
Given an integer partition of into distinct parts, the sum of the reciprocal parts is an example of an egyptian fraction. We study this statistic under the uniform measure on d…
math.NT2020
Partitions into distinct parts with bounded largest part
Walter Bridges
We prove an asymptotic formula for the number of partitions of into distinct parts where the largest part is at most for fixed . Our method follow…
math.NT2020
Limit Shapes for Unimodal Sequences
Walter Bridges
We prove asymptotic 0-1 Laws satisfied by diagrams of unimodal sequences of positive integers. These diagrams consist of columns of squares in the plane, and the upper boundary is…