Ionut Ciocan-Fontanine

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Based on the ideas in [CKP], we introduce the weighted analogue of the branching rule for the classical hook length formula, and give two proofs of this result. The first proof is completely bijective, and in a special case gives a new short combinatorial proof of the hook length formula. Our second proof is probabilistic, generalizing the (usual) hook walk(More)
Following the work of Okounkov-Pandharipande [OP1, OP2], Dia-conescu [D], and the recent work [CDKM] studying the equivariant quantum coho-mology QH * (C *) 2 (Hilb n) of the Hilbert scheme and the relative Donaldson-Thomas theory of P 1 × C 2 , we establish a connection between the J-function of the Hilbert scheme and a certain combinatorial identity in(More)
The famous hook-length formula is a simple consequence of the branching rule for the hook lengths. While the Greene-Nijenhuis-Wilf probabilistic proof is the most famous proof of the rule, it is not completely combinatorial, and a simple bijection was an open problem for a long time. In this extended abstract, we show an elegant bijective argument that(More)
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