Intervals of Permutations with a Fixed Number of Descents are Shellable

The set of all permutations, ordered by pattern containment, is a poset. We present an order isomorphism from the poset of permutations with a fixed number of descents to a certain poset of words with subword order. We use this bijection to show that intervals of permutations with a fixed number of descents are shellable, and we present a formula for the M\"obius function of these intervals. We present an alternative proof for a result on the M\"obius function of intervals $[1,\pi]$ such that $\pi$ has exactly one descent. We prove that if $\pi$ has exactly one descent and avoids 456123 and 356124, then the intervals $[1,\pi]$ have no nontrivial disconnected subintervals; we conjecture that these intervals are shellable

Insights on the spatial configuration of collective spaces within forming dynamics: the relation between infrastructure and urban transformation in Plaça de les Glòries Catalanes

The research seeks to produce insights on the spatial configuration of collective spaces where large scale infrastructure propels urban transformation. Focusing on the meaning, character and programmatic qualities of urban spaces in transformation as outcomes of fluctuating processes, it deals with complex spatial forming dynamics of urban streetscapes: the non-traditional conjugations of spaces, boundaries and territories. These spaces foster unexpected notions of proximity, territoriality, permeability and critical boundaries, investigated by means of specific parameters manifesting and interacting in time. This can help upgrade the design of architecture and urban projects to innovative techno-cultural practices and improve their integration in the urban fabric; urgent matter within the hyper-complex conditions of contemporary urban realities. The case of Plaça de les Glòries Catalanes in Barcelona, where a car-oriented open-space based on a variety of spatial manifestations turns into a formalized urban centrality, is used to unveil the complex convergence of streetscapes and urban infrastructures in contemporary urban transformations