An involution proof of the Alladi-Gordon key identity for Schur's partition theorem (Q1953452)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An involution proof of the Alladi-Gordon key identity for Schur's partition theorem |
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An involution proof of the Alladi-Gordon key identity for Schur's partition theorem (English)
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7 June 2013
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Summary: The Alladi-Gordon identity \(\sum_{k=0}^{j}(q^{i-k+1};q)_k\, {j \brack k} q^{(i-k)(j-k)}=1\) plays an important role for the Alladi-Gordon generalization of Schur's partition theorem. By using Joichi-Stanton's insertion algorithm, we present an overpartition interpretation for the Alladi-Gordon key identity. Based on this interpretation, we further obtain a combinatorial proof of the Alladi-Gordon key identity by establishing an involution on the underlying set of overpartitions.
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the Alladi-Gordon key identity
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Joichi-Stanton's insertion algorithm
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Schur's partition theorem
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overpartitions
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