Scholarlink

<p>In this article, we first investigate the partitions whose parts are congruent to <i>a</i> or <i>b</i> modulo <i>k</i> with the aid of separable integer partition classes with modulus <i>k</i> introduced by Andrews. Then, we introduce (<i>k</i>,&#xa0;<i>r</i>)-overpartitions in which only parts equivalent to <i>r</i> modulo <i>k</i> may be overlined and we will show that the number of (<i>k</i>,&#xa0;<i>k</i>)-overpartitions of <i>n</i> equals the number of partitions of <i>n</i> such that the <i>k</i>-th occurrence of a part may be overlined. Finally, we extend separable integer partition classes with modulus <i>k</i> to overpartitions and then give the generating function for (<i>k</i>,&#xa0;<i>r</i>)-modulo overpartitions, which are the (<i>k</i>,&#xa0;<i>r</i>)-overpartitions satisfying certain congruence conditions.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Separable integer partition classes and partitions with congruence conditions

  • 期刊论文

  • 发表日期：

    2025年4月15日

查看全文
  • Thomas Y. He,
  • C. S. Huang,
  • H. X. Li,
  • X. Zhang

摘要

In this article, we first investigate the partitions whose parts are congruent to a or b modulo k with the aid of separable integer partition classes with modulus k introduced by Andrews. Then, we introduce (k, r)-overpartitions in which only parts equivalent to r modulo k may be overlined and we will show that the number of (k, k)-overpartitions of n equals the number of partitions of n such that the k-th occurrence of a part may be overlined. Finally, we extend separable integer partition classes with modulus k to overpartitions and then give the generating function for (k, r)-modulo overpartitions, which are the (k, r)-overpartitions satisfying certain congruence conditions.