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<p>We study certain arithmetic properties of an analogue <i>B</i>(<i>n</i>) of Lin’s restricted partition function that counts the number of partition triples <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\pi =(\pi _1,\pi _2,\pi _3)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>π</mi> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>π</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>π</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>π</mi> <mn>3</mn> </msub> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> of <i>n</i> such that <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\pi _1\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>π</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\pi _2\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>π</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation> consist of distinct odd parts and <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\pi _3\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>π</mi> <mn>3</mn> </msub> </math></EquationSource> </InlineEquation> consists of parts divisible by 4. With the help of elementary <i>q</i>-series techniques and modular functions, we establish Ramanujan-type congruences modulo 3,&#xa0;5,&#xa0;7, and 9 for certain sums involving <i>B</i>(<i>n</i>).</p>

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Congruences for an Analogue of Lin’s Partition Function

  • 期刊论文

  • 发表日期：

    2026年4月6日

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  • Russelle Guadalupe

摘要

We study certain arithmetic properties of an analogue B(n) of Lin’s restricted partition function that counts the number of partition triples \(\pi =(\pi _1,\pi _2,\pi _3)\) π = ( π 1 , π 2 , π 3 ) of n such that \(\pi _1\) π 1 and \(\pi _2\) π 2 consist of distinct odd parts and \(\pi _3\) π 3 consists of parts divisible by 4. With the help of elementary q-series techniques and modular functions, we establish Ramanujan-type congruences modulo 3, 5, 7, and 9 for certain sums involving B(n).