Previous genetic analysis of Caulobacter crescentus showed that the periodic synthesis of hook protein, flagellin A, and flagellin B, the major flagellar subunits, is coupled in some way to chromosome replication. To examine the regulation of flagellar gene expression at the molecular level, we isolated the gene that codes for the 72,000-dalton hook protein. A specific 125I-labeled anti-hook pr...

We propose an expansion technique for weighted tree families, which unifies and extends recent results on hook-length formulas of trees obtained by Han [10], Chen et al. [3], and Yang [19]. Moreover, the approach presented is used to derive new hook-length formulas for tree families, where several hook-functions in the corresponding expansion formulas occur in a natural way. Furthermore we cons...

During early seedling development, the shoot apical meristem is protected from damage as the seedling emerges from soil by the formation of apical hook. Hook formation requires differential growth across the epidermis below the meristem in the hypocotyl. The plant hormones ethylene and auxin play key roles during apical hook development by controlling differential growth. We provide genetic and...

The apical hook of dark-grown Arabidopsis seedlings is a simple structure that develops soon after germination to protect the meristem tissues during emergence through the soil and that opens upon exposure to light. Differential growth at the apical hook proceeds in three sequential steps that are regulated by multiple hormones, principally auxin and ethylene. We show that the progress of the a...

Certain Drosophila embryonic epidermal cells construct actin-based protrusions, called denticles, which exhibit stereotyped, column-specific differences in size, density and hook orientation. This precise denticle pattern is conserved throughout all drosophilids yet studied, and screening for mutations that affect this pattern has been used to identify genes involved in development and signalin...

— We discover another one-parameter generalization of Postnikov's hook length formula for binary trees. The particularity of our formula is that the hook length h v appears as an exponent. As an application, we derive another simple hook length formula for binary trees when the underlying parameter takes the value 1/2.

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...