An integer partition λ ` n corresponds, via its Ferrers diagram, to an artinian monomial ideal I ⊂ C[x, y] with dimC C[x, y]/I = n. If λ corresponds to an integrally closed ideal we call it concave . We study generating functions for the number of concave partitions, unrestricted or with at most r parts. 1. concave partitions By an integer partition λ = (λ1, λ2, λ3, . . . ) we mean a weakly dec...

Latin has a large group of derivatives whose suffixes appear to attach to the stem of the verb’s passive participle. The agent noun caesor ‘cutter’ is an example: inside caesor there is a stem caesthat is identical to that of the participle caesus, -ī ‘which has been cut-masc.-sg’, from the verb caedere. The same stem caesappears in other derivatives: caesiō ‘an act of cutting’, caesūra ‘a cutt...

Given a positive integer n, and partitions λ and μ of n, let Kλμ denote the Kostka number, which is the number of semistandard Young tableaux of shape λ and weight μ. Let J(λ) denote the number of μ such that Kλμ = 1. By applying a result of Berenshtein and Zelevinskii, we obtain a formula for J(λ) in terms of restricted partition functions, which is recursive in the number of distinct part siz...

“bēstūn” other than a place name is the name of a noble lady mentioned in the pahlavi book of ayādgār ī zarērān. this article presents the author’s revised method of reading the middle persian version of the ancient *baga-stāna- in the sassanian book pahlavi sources and tries to give a clear view on the signification and cultural background of this name as well as tracing it down to the culture...