We generalize multivariate hook product formulae for P -partitions. We use Macdonald symmetric functions to prove a (q, t)-deformation of Gansner’s hook product formula for the generating functions of reverse (shifted) plane partitions. For a d-complete poset, we present a conjectural (q, t)-deformation of Peterson–Proctor’s hook product formula.

Berele and Regev [1] defined the ring of hook Schur functions and showed that these functions are the characters of the general Lie superalgebra. Since the introduction of the hook Schur functions they have been extensively studied with respect to their combinatorial properties [2], [3], [4]. We compute the Hilbert series of this ring by giving a generating function for the partitions which fit...

Until now, identification of components of the flagellar protein export apparatus has been indirect. We have now identified these components directly by establishing whether mutants defective in putative export components could translocate export substrates across the cytoplasmic membrane into the periplasmic space. Hook-type proteins could be exported to the periplasm of rod mutants, indicatin...

BACKGROUND Left double-lumen tracheal tubes (DLTs), with or without a hook to engage the carina, remain the standard device for lung isolation during anaesthesia. OBJECTIVE The purpose of the study was to compare these DLTs with and without a hook. DESIGN A randomised, controlled, single-blinded study. SETTING University hospital. PARTICIPANTS One hundred and eighty-four patients underg...

We generalize multivariate hook product formulae for P -partitions. We use Macdonald symmetric functions to prove a (q, t)-deformation of Gansner’s hook product formula for the generating functions of reverse (shifted) plane partitions. (The unshifted case has also been proved by Adachi.) For a d-complete poset, we present a conjectural (q, t)-deformation of Peterson–Proctor’s hook product form...

Olympic archers use different hook techniques like upper and lower two-finger hook. So, the purpose of this study is to compare three different hook techniques in archery by using kinetic and kinematic methods. A high level archer (FITA scores > 1300) volunteered to participate in this study. The subject engaged in a single test session consisting of 6 shots. Nine forearm and shoulder girdle mu...

BACKGROUND Post-copulatory sexual selection has been shown to shape morphology of male gametes. Both directional and stabilizing selection on sperm phenotype have been documented in vertebrates in response to sexual promiscuity. METHODOLOGY Here we investigated the degree of variance in apical hook length and tail length in six taxa of murine rodents. CONCLUSIONS Tail sperm length and apica...