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This paper makes a combinatorial study of the two monoids and the two types of tableaux that arise from the two possible generalizations of the Patience Sorting algorithm from permutations (or standard words) to words. For both types of tableaux, we present Robinson--Schensted--Knuth-type correspondences (that is, bijective correspondences between word arrays and certain pairs of semistandard tableaux of the same shape), generalizing two known correspondences: a bijective correspondence between standard words and certain pairs of standard tableaux, and an injective correspondence between words and pairs of tableaux.

We also exhibit formulas to count both the number of each type of tableaux with given evaluations (that is, containing a given number of each symbol). Observing that for any natural number $n$, the $n$-th Bell number is given by the number of standard tableaux containing $n$ symbols, we restrict the previous formulas to standard words and extract a formula for the Bell numbers. Finally, we present a `hook length formula' that gives the number of standard tableaux of a given shape and deduce some consequences.

In this paper we characterize the monoids of endomorphisms of the semigroups PO_n and POI_n of all order-preserving partial transformations and of all order-preserving partial permutations, respectively, of a finite n-chain.

This chapter provides an overview of the alpha paleobiodiversity of Angola based on the available fossil record that is limited to the sedimentary rocks, ranging in age from Precambrian to the present. The geological period with the highest paleobiodiversity in the Angolan fossil record is the Cretaceous, with more than 80{%} of the total known fossil taxa, especially marine molluscs, including ammonites as a majority among them. The vertebrates represent about 15{%} of the known fauna and about one tenth of them are species firstly described based on specimens from Angola.

Late Jurassic theropod tracks are very common both in North Africa and Europe. Two recently described ichnotaxa Megalosauripus transjuranicus and Jurabrontes curtedulensis from the Kimmeridgian of Switzerland show the coexistence of two apex predators in the same palaeoenvironment. Similar tracks can be found in tracksites from the Iberian Peninsula and from Morocco. Here, we further explore the similarities among the Swiss ichnotaxa and the other tracks from Germany (Kimmeridgian), Spain (Tithonian-Berriasian), Portugal (Oxfordian-Tithonian) and Morocco (Kimmeridgian) through novel three-dimensional data comparisons. Specimens were grouped in two morphotypes: 1) large and gracile (30 < Foot Length<50 cm) and 2) giant and robust (FL > 50 cm). The analyses show a great morphological overlap among these two morphotypes and the Swiss ichnotaxa (Megalosauripus transjuranicus and Jurabrontes curtedulensis, respectively), even despite the differences in sedimentary environment and age. This suggests a widespread occurrence of similar ichnotaxa along the western margin of Tethys during the Late Jurassic. The new data support the hypothesis of a Gondwana-Laurasia faunal exchange during the Middle or early Late Jurassic, and the presence of migratory routes around the Tethys.

The left patience sorting (lPS) monoid, also known in the literature as the Bell monoid, and the right patient sorting (rPS) monoid are introduced by defining certain congruences on words. Such congruences are constructed using insertion algorithms based on the concept of decreasing subsequences.
Presentations for these monoids are given.

Each finite-rank rPS monoid is shown to have polynomial growth and to satisfy a non-trivial identity (dependent on its rank), while the infinite rank rPS monoid does not satisfy a non-trivial identity. The lPS monoids of finite rank have exponential growth and thus do not satisfy non-trivial identities. The
complexity of the insertion algorithms is discussed.

rPS monoids of finite rank are shown to be automatic and to have recursive complete presentations. When the rank is $1$ or $2$, they are also biautomatic. lPS monoids of finite rank are shown to have finite complete presentations and to be biautomatic.

Este capítulo apresenta uma visão geral da paleobiodiversidade alfa de Angola com base no registo fóssil disponível, o qual se limita às rochas sedimentares, a sua idade variando entre o Pré‑Câmbrico e o pre‑
sente. O período geológico com a maior paleobiodiversidade no registo fóssil angolano é o Cretácico, com mais de 80% do total dos táxones fósseis conhecidos, especialmente moluscos marinhos, sendo estes na sua maioria
amonites. Os vertebrados representam cerca de 15% da fauna conhecida e cerca de um décimo destes são espécies descritas pela primeira vez com base em espécimes de Angola.