Recently, a simple proof of the hook length formula was given via the branching rule. In this paper, we extend the results to shifted tableaux. We give a bijective proof of the branching rule for the hook lengths for shifted tableaux; present variants of this rule, including weighted versions; and make the first tentative steps toward a bijective proof of the hook length formula for d-complete ...

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...

Percutaneous preoperative localisation of breast tumours using a hook-wire needle is a standard radiological practice. The use of a hook-wire in preoperative localisation of pulmonary nodules under computed tomography guidance has also been described in overseas publications. We describe herein our local experience with the use of a hook-wire needle that is primarily used in breast tumours in p...

Common obstacles to successful retrieval of retrievable inferior vena cave filter include embedded filter hook and severe tilt of the filter. We described a modified wire-loop snare technique using self-made fishhook-like pigtail catheter and 11-F-long sheath to retrieve a severe tilted filter with embedded hook successfully. The modified wire-loop snare technique is simple and effective requir...

The structural polarity of cellular microtubules can be visualized in situ by lysing cells in special buffers containing tubulin. Under these conditions, the tubulin polymerizes to form curved sheets which attach to the walls of the endogenous microtubules. When such decorated microtubules are cut in cross section and viewed in the electron microscope, they appear to bear hooks curving clockwis...

BACKGROUND Video-assisted thoracic surgery (VATS) is currently performed to diagnose and treat solitary pulmonary nodules (SPN). However, the intra-operative identification of deep nodules can be challenging with VATS as the lung is difficult to palpate. The aim of the study was to report the utility and the results of pre-operative computed tomography (CT)-guided hook wire localization of SPN....