On the number of equivalence classes of bi-partitions arising from the color change (Q6548280)
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scientific article; zbMATH DE number 7858241
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the number of equivalence classes of bi-partitions arising from the color change |
scientific article; zbMATH DE number 7858241 |
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On the number of equivalence classes of bi-partitions arising from the color change (English)
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1 June 2024
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In this paper, the author introduces a new class of bi-partition functions, denoted as \( c_k(n) \), which counts the number of bi-color partitions of \( n \), where the second color appears only in parts that are multiples of \( k \). Two partitions are considered equivalent if they can be transformed into one another by switching the color of parts that are congruent to zero modulo \( k \). The author demonstrates that the generating function for \( c_k(n) \) involves a partial theta function.
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color change
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bi-partition
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partial theta function
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congruence
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