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Thirteen Planothidium species are illustrated and discussed in a detailed morphological account based on light and scanning electron microscopy analysis of modern and historic materials related to the names Planothidium rostratum (Østrup) Lange-Bertalot and Planothidium frequentissimum (Lange-Bertalot) Lange-Bertalot. Eight species from freshwater environments in Europe, Asia and South America are proposed as new. All taxa here discussed and illustrated belong to the group of species characterized by the presence of a cavum in the rapheless valve. Additional information concerning their distribution and ecology is briefly commented based on a thorough literature revision.

Abstract:The Island of Majorca (Spain) is characterized by a Mediterranean climate and a karstic geology that favors the formation of numerous springs and spring-fed streams on the island's Northwester zone. Water and epilithic diatom samples were collected from two springs and four spring-fed streams, located at altitudes ranging from 0 to 756 m a.s.l., in different seasons between 2005 and 2008. Water chemistry in these systems is characterized by high concentrations of dissolved calcium and pH values ranging from 6.6 to 8.4. A total of 111 diatom taxa belonging to 40 genera were found and the most abundant taxa were illustrated with LM and SEM. The diatom communities of the studied sites were dominated by species such as Achnanthidium minutissimum, A. pyrenaicum, Amphora pediculus, Cymbella vulgata, Diploneis separanda, Encyonopsis minuta, Gomphonema lateripunctatum and Navicula cryptotenella, reflecting the calcareous geological nature of Majorca Island. In the framework of the study 22 diatom taxa, which are new for Balearic Islands were recorded, such as Achnanthidium straubianum, Amphora indistincta, Cymbella lange-bertalotii, Encyonopsis subminuta, Karayevia kolbei, Navicula aff. margalithii, N. reichardtiana and N. subalpina. In addition, a new freshwater diatom species belonging to the genus Cymbopleura, C. margalefii was found in the Torrente of Deià. Cymbopleura margalefii is described as a new species based on LM and SEM observations, and compared with similar taxa. A checklist of the 309 diatom taxa recorded so far from the Balearic Islands is also presented.

The set of Dyck paths of length 2n inherits a lattice structure from a bijection with the set of noncrossing partitions with the usual partial order. In this paper, we study the joint distribution of two statistics for Dyck paths: area (the area under the path) and rank (the rank in the lattice).While area for Dyck paths has been studied, pairing it with this rank function seems new, and we get an interesting (q, t)-refinement of the Catalan numbers. We present two decompositions of the corresponding generating function: one refines an identity of Carlitz and Riordan; the other refines the notion of γ-nonnegativity, and is based on a decomposition of the lattice of noncrossing partitions due to Simion and Ullman.Further, Biane's correspondence and a result of Stump allow us to conclude that the joint distribution of area and rank for Dyck paths equals the joint distribution of length and reflection length for the permutations lying below the n-cycle (12 · · · n) in the absolute order on the symmetric group.