Over the past two decades, real GDP per capita in Portugal has nearly stagnated. The conventional account attributes this to the mismanagement of public finances and the lack of structural reforms in ...labor and product markets prior to the "adjustment program" agreed with the troika in the early 2010s. In the same vein, the neoclassical-inspired interpretation explains the subsequent recovery based on supply-side and fiscal reforms implemented during the troika years, which would account for the reduced fiscal deficits, external equilibrium and employment growth registered in the pre-COVID-19 period. In this article, we challenge this optimistic view, identifying structural weaknesses of the Portuguese economy that would have soon become apparent even if the pandemic had not happened. Addressing these weaknesses requires changes that go beyond the EU and national responses to the pandemic crisis.
Industrial dynamics and labor mobility are two fields of economic research that have developed fast in recent years, but along what are essentially separate lines. This article shows that the ...processes those two fields deal with can be highly interdependent, and discusses the usefulness of, and the opportunity for, an integrated approach to the dynamics of industries and labor mobility. It concludes with a list of questions that inform a research agenda dedicated to such approach.
Any permutation w of the symmetric group can be generated by a product of adjacent transpositions, and a reduced word for w is a sequence of generators of minimal length whose product is w. The main ...result in this paper gives a formula to compute the diameter of a commutation class of the graph G(w), whose vertices are reduced words for w and whose edges are braid relations. To do so, we use a set-valued metric on the set of all reduced words of a given permutation which turn out to induce the usual distance in any commutation class. If a permutation is fully commutative, i.e. it has only one commutation class, then the formula gives the diameter of G(w). The diameter for a Grassmanian permutation is also given in terms of its Lehmer code.
The total number of noncrossing partitions of type $\Psi$ is the $n$th Catalan number $\frac{1}{ n+1} \binom{2n}{n}$ when $\Psi =A_{n-1}$, and the binomial coefficient $\binom{2n}{n}$ when $\Psi ...=B_n$, and these numbers coincide with the correspondent number of nonnesting partitions. For type $A$, there are several bijective proofs of this equality; in particular, the intuitive map, which locally converts each crossing to a nesting, is one of them. In this paper we present a bijection between nonnesting and noncrossing partitions of types $A$ and $B$ that generalizes the type $A$ bijection that locally converts each crossing to a nesting.
Le nombre total des partitions non-croisées du type $\Psi$ est le $n$-ème nombre de Catalan $\frac{1}{ n+1} \binom{2n}{n}$ si $\Psi =A_{n-1}$, et le coefficient binomial $\binom{2n}{n}$ si $\Psi =B_n$, et ces nombres son coïncidents avec le nombre correspondant des partitions non-emboîtées. Pour le type $A$, il y a plusieurs preuves bijectives de cette égalité; en particulier, la intuitive fonction, qui convertit localement chaque croisée en une emboîtée, c'est un d'entre eux. Dans ce papier nous présentons une bijection entre partitions non-croisées et non-emboîtées des types $A$ et $B$ qui généralise la bijection du type $A$ qui localement convertit chaque croisée en une emboîtée.
We present combinatorial Gray codes and explicit designs of efficient algorithms for lexicographical combinatorial generation of the sets of nonnesting and sparse nonnesting set partitions of length ...n.
Neste texto discutem-se explicações alternativas para a crise que atingiu a zona euro em 2010-2012. A crise é indissociável da acumulação de desequilíbrios externos entre países membros desde meados ...dos anos 90. Assim, a explicação para as suas origens tem de passar pela identificação dos mecanismos que contribuíram para a acumulação daqueles desequilíbrios. As diferentes explicações discutidas – a convergência entre economias, as práticas orçamentais, as relações laborais, os fluxos de capitais e os perfis de especialização – não são mutuamente exclusivas. No entanto, os dados disponíveis sugerem que há processos mais relevantes do que outros – e não são os mais óbvios.
The paper discusses alternative explanations for the crisis that hit the euro area in 2010-2012. The crisis is inseparable from the accumulation of external imbalances between member countries since the mid-1990s. Therefore, the explanation for its origins has to be found in the identification of the mechanisms that contributed to the accumulation of those imbalances. The different explanations discussed here – convergence between economies, fiscal practices, labour relations, capital flows and specialization profiles – are not mutually exclusive. However, the available evidence suggests that some processes are more relevant than others – and they are not the most obvious.
Using the standard Coxeter presentation for the signed symmetric group Sn+1B on n+1 letters, two reduced expressions for a given signed permutation are in the same commutation class if one expression ...can be obtained from the other one by applying a finite sequence of commutations. The commutative classes of a given signed permutation can be seen as the vertices of a graph, called the commutation graph, where two classes are connected by an edge if there are elements in those classes that differ by a long braid relation. We define a rank function for the commutation graph for the longest signed permutation, and use this function to compute the diameter and the radius of the graph. We also prove that the commutation graph for the longest signed permutation is not planar for n>2, and identify the classes with a single element.
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