It is well-known that Catalan numbers Cn = 1 n+1 ( 2n n ) count the number of dominant regions in the Shi arrangement of type A, and that they also count partitions which are both n-cores as well as (n + 1)-cores. These concepts have natural extensions, which we call here the m-Catalan numbers and m-Shi arrangement. In this paper, we construct a bijection between dominant regions of the m-Shi a...

Four Valiatrella species, Valiatrella pulchra (Gorochov, 1985), Valiatrella sororia (Gorochov, 2002), Valiatrella laminaria Liu & Shi, 2007 and Valiatrella multiprotubera Liu & Shi, 2007, recorded from China are reviewed. A new species, Valiatrella persicifolius sp. nov., is described and illustrated.