We give formulae for computing Kronecker coefficients occurring in the expansion of sμ ∗ sν , where both μ and ν are nearly rectangular, and have smallest parts equal to either 1 or 2. In particular, we study s(n,n−1,1) ∗ s(n,n), s(n−1,n−1,1) ∗ s(n,n−1), s(n−1,n−1,2) ∗ s(n,n), s(n−1,n−1,1,1) ∗ s(n,n) and s(n,n,1) ∗ s(n,n,1). Our approach relies on the interplay between manipulation of symmetric...

We show that the Eulerian-Catalan numbers enumerate Dyck permutations. We provide two proofs for this fact, the first using the geometry of alcoved polytopes and the second a direct combinatorial proof via an Eulerian-Catalan analogue of the Chung-Feller theorem.

Abstract Despite its vulnerable position as a minoritised language, the presence of Catalan in digital sphere is relatively strong, thanks to an active online community with high technological profile. Technological support for slowly growing, following recent advances AI and increased awareness value language data technologies among public private bodies. However, more effort needed promote cr...

We compared the genetic diversity and distance among six German draught horse breeds to wild (Przewalski's Horse), primitive (Icelandic Horse, Sorraia Horse, Exmoor Pony) or riding horse breeds (Hanoverian Warmblood, Arabian) by means of genotypic information from 30 microsatellite loci. The draught horse breeds included the South German Coldblood, Rhenish German Draught Horse, Mecklenburg Cold...