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Signed differential posets and sign-imbalance

Thomas Lam
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Abstract

We study signed differential posets, a signed version of differential posets. These posets satisfy enumerative identities which are signed analogues of those satisfied by differential posets. Our main motivations are the sign-imbalance identities for partition shapes originally conjectured by Stanley, now proven by Lam, Reifergerste and Sjostrand. We show that these identities result from a signed differential poset structure on Young's lattice, and explain similar identities for Fibonacci shapes.

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Thomas Lam. 2006-12-11. Signed differential posets and sign-imbalance. https://arxiv.org/abs/math/0611296

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