Short, bijective proofs of identities for multisets of ‘hook pairs’ (arm-leg pairs) of the cells of certain diagrams are given. These hook pair identities were originally found by Regev.

We present characteristic-free resolutions and splitting homotopies for the Weyl modules associated to skew-hook shapes. Résumé. Nous présentons des résolutions en caractéristique-libre, et des homotopies associées aux formes du type “skew-hook”.

Two cases of fish hook injuries to the eye are described. Both were removed successfully by rotating the hook through undamaged tissue before snipping off the barb. Good vision was restored without complications for periods of 12 and 18 months.

In this study the cleavage divisions and the ultrastructural analysis of early embryos as well as cellular organisation of infective oncosphere of the anoplocephalid cestode Mosgovoyia ctenoides are described. The early cleavage is unequal and results in the formation of three types of blastomeres: 2 large macromeres containing large electron dense granules, 3 medium-size mesomeres and several ...

ABSTRACT The Tesler matrices with hook sums (a1, a2, . . . , an) are non-negative integral upper triangular matrices, whose i diagonal element plus the sum of the entries in the arm of its (french) hook minus the sum of the entries in its leg is equal to ai for all i. In a recent paper [6], the second author expressed the Hilbert series of the Diagonal Harmonic modules as a weighted sum of the ...

Many textbooks contain material on partitions. Two standard references are [A] and [S]. A partition of a natural integer n with parts λ1, . . . , λk is a finite decreasing sequence λ = (λ1 ≥ λ2 ≥ · · · ≥ λk > 0) of natural integers λ1, . . . , λk > 0 such that n = ∑k i=1 λi. We denote by |λ| the content n of λ. Partitions are also written as sums: n = λ1 + · · ·+ λk and one uses also the (abusi...

Abstract In this article, we evaluate determinants of “block hook” matrices, which are block matrices consist hook matrices. particular, deduce that the determinant a matrix factorizes nicely. addition give combinatorial interpretation aforesaid factorization property by counting weighted paths in suitable digraph.

We present here for the first time the crystal structure of an AT-hook domain. We show the structure of an AT-hook of the ubiquitous nuclear protein HMGA1, combined with the oligonucleotide d(CGAATTAATTCG)(2), which has two potential AATT interacting groups. Interaction with only one of them is found. The structure presents analogies and significant differences with previous NMR studies: the AT...