bibkey: bhoria2026missing
authors: Subhash Chand Bhoria, Pramod Eyyunni, Subhrangsu Santra
year: 2026
title: 'On the number of missing integers in partitions'
doi: 10.48550/arXiv.2604.12557
url: https://arxiv.org/abs/2604.12557v1
claim: "Question 3 asks for a concise overpartition analogue of the all-threshold missing-size statistic in Theorem 2.9."
strata_touched:
  - D5/S3/Combinatorics/Partitions/OverpartitionThreshold
license: citation-only
triage: anchor

On the number of missing integers in partitions

Section 4, Question 3:

Is there an overpartition analogue of Theorem 2.9, namely, a concise identity for the number of integers less than or equal to the largest part that appear less than k times in all overpartitions of n.

An overpartition permits an optional overline on the first occurrence of each distinct part size. Multiplicity includes that occurrence. A positive size absent from the partition has multiplicity zero and is included in the statistic when it lies below the largest part. The empty-partition convention in the formal source extends the statistic by largest part zero.

Question 3 requests an identity; it does not conjecture a particular proposed formula. The congruence and asymptotic questions in the same section are separate.

Verified locator

DOI: 10.48550/arXiv.2604.12557

URL: https://arxiv.org/abs/2604.12557v1

Locator: https://arxiv.org/html/2604.12557v1 , Section 2.4, Theorem 2.9, and Section 4, Question 3.