Position Sequences and a $q$-Analogue for the Modular Hook Length Formula

The weighted hook length formula

Abstract. 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 proof of Green-Nijenhuis-Wi...

Hook Length Formula and Geometric Combinatorics

A mixed hook-length formula for affine Hecke algebras

Let Ĥ l be the affine Hecke algebra corresponding to the group GLl over a p-adic field with residue field of cardinality q . We will regard Ĥ l as an associative algebra over the field C(q). Consider the Ĥ l+m -module W induced from the tensor product of the evaluation modules over the algebras Ĥ l and Ĥm . The module W depends on two partitions λ of l and μ of m, and on two non-zero elements o...

A direct bijective proof of the hook-length formula

The aim of this paper is to give a bijective proof of the hook-length formula for the enumeration of standard Young tableaux of a given shape. This formula was discovered by Frame, Robinson and Thrall in 1954 [1] and since then it has been the object of much study. Many proofs have been published based on different approaches, but none of them is considered satisfactory. We refer to the paper [...

A Simple Proof of the Hook Length Formula

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