Euler's partition theorem and the combinatorics of -sequences
Euler's partition theorem and the combinatorics of -sequences
Euler's partition theorem and the combinatorics of -sequences
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The Lecture Hall Theorem [BME1] The generating function for<br />
integer <strong>sequences</strong> λ 1 , λ 2 , . . . , λ n satisfying:<br />
is<br />
L n :<br />
λ 1<br />
n ≥ λ 2<br />
n − 1 ≥ . . . ≥ λ n<br />
1 ≥ 0<br />
L n (q) =<br />
n∏<br />
i=1<br />
1<br />
1 − q 2i−1