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<p>We consider a sequence of integer partitions wherein the smallest part is fixed and its first occurrence may be overlined. Among the results, we prove identities and positivity for this sequence and its weighted versions. As a consequence, we deduce inequalities of integer partitions and we establish Legendre type formulas. Furthermore, we give a full description modulo 2 for our sequences.</p>

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On Integer Partitions with a Fixed Overlined Smallest Part

  • 期刊论文

  • 发表日期：

    2025年12月15日

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  • George E. Andrews,
  • Mohamed El Bachraoui

摘要

We consider a sequence of integer partitions wherein the smallest part is fixed and its first occurrence may be overlined. Among the results, we prove identities and positivity for this sequence and its weighted versions. As a consequence, we deduce inequalities of integer partitions and we establish Legendre type formulas. Furthermore, we give a full description modulo 2 for our sequences.