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<p>G. E. Andrews recently proved congruences (first conjectured by Beck) for <i>NT</i>(<i>m</i>,&#xa0;<i>k</i>,&#xa0;<i>n</i>) called Andrews-Beck partition statistic, which denotes the total number of parts in the partitions of <i>n</i> with rank congruent to <i>m</i> modulo <i>k</i>. Motivated by this work, arithmetic properties of this statistic and their analogs are widely studied. In this paper, we consider Andrews-Beck partition statistic for MacMahon’s modular partitions. Equalities, identities and congruences for this new statistic are obtained.</p>

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Andrews-beck partition statistics for modular partitions

  • 期刊论文

  • 发表日期：

    2026年2月18日

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  • Renrong Mao

摘要

G. E. Andrews recently proved congruences (first conjectured by Beck) for NT(m, k, n) called Andrews-Beck partition statistic, which denotes the total number of parts in the partitions of n with rank congruent to m modulo k. Motivated by this work, arithmetic properties of this statistic and their analogs are widely studied. In this paper, we consider Andrews-Beck partition statistic for MacMahon’s modular partitions. Equalities, identities and congruences for this new statistic are obtained.