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<p>In this paper, we give a new combinatorial interpretation for the Rogers–Ramanujan–Gordon partitions for <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="26_2025_745_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="41" /> </InlineMediaObject> <EquationSource Format="TEX">\(k=3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>k</mi> <mo>=</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation>. Our interpretation is given by base partition and moves ideas. We conclude the paper with some research questions related to the generalization of this approach.</p>

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A Combinatorial Interpretation of the Series for Rogers–Ramanujan–Gordon Identities when \(k=3\)

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  • 发表日期：

    2025年2月26日

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摘要

In this paper, we give a new combinatorial interpretation for the Rogers–Ramanujan–Gordon partitions for \(k=3\) k = 3 . Our interpretation is given by base partition and moves ideas. We conclude the paper with some research questions related to the generalization of this approach.