An Involution Proof of the Alladi-Gordon Key Identity for Schur's Partition Theorem
نویسنده
چکیده
The Alladi-Gordon identity ∑j k=0(q i−k+1; q)k [ j 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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ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 20 شماره
صفحات -
تاریخ انتشار 2013