Dynamical aspects of σ\sigma-machines

The $\sigma$-machine was recently introduced by Cerbai, Claesson and Ferrari as a tool to gain a better insight on the problem of sorting permutations with two stacks in series. It consists of two consecutive stacks, which are restricted in the sense that their content must at all times avoid a certain pattern: a given $\sigma$, in the first stack, and $21$, in the second. Here we prove that in most cases sortable permutations avoid a bivincular pattern $\xi$. We provide a geometric decomposition of $\xi$-avoiding permutations and use it to count them directly. Then we characterize the permutations with the property that the output of the $\sigma$-avoiding stack does not contain $\sigma$, which we call effective. For $\sigma=123$, we obtain an alternative method to enumerate sortable permutations. Finally, we classify $\sigma$-machines and determine the most challenging to be studied.Comment: 19 pages, 4 figures, 3 tables. arXiv admin note: text overlap with arXiv:2210.0362

Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations

Defant, Engen, and Miller defined a permutation to be uniquely sorted if it has exactly one preimage under West's stack-sorting map. We enumerate classes of uniquely sorted permutations that avoid a pattern of length three and a pattern of length four by establishing bijections between these classes and various lattice paths. This allows us to prove nine conjectures of Defant.Comment: 18 pages, 16 figures, new version with updated abstract and reference

The Brownian limit of separable permutations

We study random uniform permutations in an important class of pattern-avoiding permutations: the separable permutations. We describe the asymptotics of the number of occurrences of any fixed given pattern in such a random permutation in terms of the Brownian excursion. In the recent terminology of permutons, our work can be interpreted as the convergence of uniform random separable permutations towards a "Brownian separable permuton".Comment: 45 pages, 14 figures, incorporating referee's suggestion

Combinatorial generation via permutation languages

In this work we present a general and versatile algorithmic framework for exhaustively generating a large variety of different combinatorial objects, based on encoding them as permutations. This approach provides a unified view on many known results and allows us to prove many new ones. In particular, we obtain the following four classical Gray codes as special cases: the Steinhaus-Johnson-Trotter algorithm to generate all permutations of an $n$-element set by adjacent transpositions; the binary reflected Gray code to generate all $n$-bit strings by flipping a single bit in each step; the Gray code for generating all $n$-vertex binary trees by rotations due to Lucas, van Baronaigien, and Ruskey; the Gray code for generating all partitions of an $n$-element ground set by element exchanges due to Kaye. We present two distinct applications for our new framework: The first main application is the generation of pattern-avoiding permutations, yielding new Gray codes for different families of permutations that are characterized by the avoidance of certain classical patterns, (bi)vincular patterns, barred patterns, Bruhat-restricted patterns, mesh patterns, monotone and geometric grid classes, and many others. We thus also obtain new Gray code algorithms for the combinatorial objects that are in bijection to these permutations, in particular for five different types of geometric rectangulations, also known as floorplans, which are divisions of a square into $n$ rectangles subject to certain restrictions. The second main application of our framework are lattice congruences of the weak order on the symmetric group~$S_n$. Recently, Pilaud and Santos realized all those lattice congruences as $(n-1)$-dimensional polytopes, called quotientopes, which generalize hypercubes, associahedra, permutahedra etc. Our algorithm generates the equivalence classes of each of those lattice congruences, by producing a Hamilton path on the skeleton of the corresponding quotientope, yielding a constructive proof that each of these highly symmetric graphs is Hamiltonian. We thus also obtain a provable notion of optimality for the Gray codes obtained from our framework: They translate into walks along the edges of a polytope

Combinatorial generation via permutation languages. I. Fundamentals

In this work we present a general and versatile algorithmic framework for exhaustively generating a large variety of different combinatorial objects, based on encoding them as permutations. This approach provides a unified view on many known results and allows us to prove many new ones. In particular, we obtain the following four classical Gray codes as special cases: the Steinhaus-Johnson-Trotter algorithm to generate all permutations of an $n$-element set by adjacent transpositions; the binary reflected Gray code to generate all $n$-bit strings by flipping a single bit in each step; the Gray code for generating all $n$-vertex binary trees by rotations due to Lucas, van Baronaigien, and Ruskey; the Gray code for generating all partitions of an $n$-element ground set by element exchanges due to Kaye. We present two distinct applications for our new framework: The first main application is the generation of pattern-avoiding permutations, yielding new Gray codes for different families of permutations that are characterized by the avoidance of certain classical patterns, (bi)vincular patterns, barred patterns, boxed patterns, Bruhat-restricted patterns, mesh patterns, monotone and geometric grid classes, and many others. We also obtain new Gray codes for all the combinatorial objects that are in bijection to these permutations, in particular for five different types of geometric rectangulations, also known as floorplans, which are divisions of a square into $n$ rectangles subject to certain restrictions. The second main application of our framework are lattice congruences of the weak order on the symmetric group~$S_n$. Recently, Pilaud and Santos realized all those lattice congruences as $(n-1)$-dimensional polytopes, called quotientopes, which generalize hypercubes, associahedra, permutahedra etc. Our algorithm generates the equivalence classes of each of those lattice congruences, by producing a Hamilton path on the skeleton of the corresponding quotientope, yielding a constructive proof that each of these highly symmetric graphs is Hamiltonian. We thus also obtain a provable notion of optimality for the Gray codes obtained from our framework: They translate into walks along the edges of a polytope

Análisis de accesibilidad de plantillas y sitios web de revistas académicas de impacto

Las revistas académicas europeas deben cumplir con las dos directivas aprobadas por la Unión Europea para garantizar la accesibilidad digital al tratarse de publicaciones electrónicas. En el proceso de publicación, las revistas facilitan a los autores unas plantillas que deben ser accesibles. Sin embargo, los autores tienen la responsabilidad de hacer su trabajo final accesible. Este trabajo explora si se cumple con los criterios de accesibilidad digital en todas las etapas, desde la elaboración de las plantillas hasta la publicación definitiva de edición, tanto si se hace en PDF o en versión web.European academic journals must comply with the two directives approved by the European Union to ensure digital accessibility as electronic publications. In the publication process, journals provide authors with templates that must be accessible. However, authors have the responsibility to make their final work accessible. This paper explores if digital accessibility criteria are met at all stages, from the development of the templates to the final publication of the edition, whether in PDF or web version.Grado en Ingeniería en Sistemas de Informació

Understanding key geological processes and controls on cold-water coral habitat development in submarine canyons

Cold-water corals are sessile, filter-feeding organisms that baffle water flow inducing sedimentation around their framework. Through geological time, should environmental conditions permit, they can produce positive topographic features on the seafloor called mounds through successive and persistent reef development. These reef ecosystems are considered biodiversity “hotspots” between 200 and 1000 m in the Atlantic Ocean. They are regarded as vulnerable marine ecosystems, providing essential ecosystem services. Over the past two decades, a considerable body of information has been accumulated on understanding the temporal development of CWC reef and mound formation. However, this research is limited in resolution, the range of study sites and datasets analysed. Here, an assessment of the temporal variation of CWC reefs and mounds situated in the west Porcupine Bank (wPB) and Porcupine Bank Canyon (PBC) is presented as well as background palaeoenvironmental information from an off-mound core. Previous studies of the spatial distribution of reefs and mounds reveal that they are dispersed across a variety of geomorphological settings in the region, including the canyon head, along the canyon lip and on the bank. This research broadly aims to understand the temporal distribution of the coral habitats within these contrasting settings. In 2015 and 2016, the QuERCi I and QuERCi II research cruises attempted coring the substrates of the canyon using traditional methods (i.e. gravity and box-corers). However, the acquired cores were insufficient in size and lacked an understanding of what habitat they were taken from. As such, 2 more research cruises (CoCoHaCa I and CoCoHaCa II) were carried out in 2017 and 2018 using sophisticated novel coring systems (ROV-vibrocoring). These methods proved successful, and cores were acquired through various CWC habitats in the canyon (mound summits, flanks, bank, slope and foot of the slope) and presented herein. This data includes novel 3-dimensional computed tomography (CT) derived imagery alongside traditional sedimentological approaches. The CT imagery was used to classify reef and mound formation/cessation. The cores were then split, sampled and investigated using a series of analytical techniques. The phases of formation/cessation were first constrained using radiocarbon dating and the cores were subsequently examined using grain size analysis to interpret the hydrodynamic regime. Stable isotope analysis on planktic and benthic foraminifera was then used to investigate paleoenvironmental conditions, which were contextualized by benthic foraminifera assemblages. An off-mound core was examined to elucidate the impact of the (de)glaciation of the British-Irish Ice Sheet (BIIS) on the wPB. Analysis of the core revealed that several fluxes of ice-rafted debris were deposited to the site. It was found that bottom currents became sluggish during stadial phases. Evidence for iceberg scouring in the core was also identified. Two coral bearing cores acquired from mound summits of variable distance to the canyon were then analysed. It was found that mound growth was twice as fast on the canyon lip than mounds 1 km away on the wPB. Multiproxy data revealed that a high food signal occurs closer to the canyon. This suggests that submarine canyons play a key role in enhancing particle supply and therefore influences coral growth and mound developmenton the margin. The radiocarbon dates acquired from coral bearing cores on the wPB suggest that corals occupied the bank since at least 45.1 ka BP. This finding subsequently resulted in revising our understanding of CWC re-expansion into the NE Atlantic during favourable climatic conditions, highlighting the crucial role played by submarine canyons. Findings outlined in this thesis provides the scientific community with new insights into the tolerances of cold-water corals during ecological tipping points. Furthermore, it highlights the need to investigate other submarine canyons occupied by CWCs in the NE Atlantic using ROV-vibrocoring

Catalan and Schröder permutations sortable by two restricted stacks

International audienc

LIPIcs, Volume 248, ISAAC 2022, Complete Volume

LIPIcs, Volume 248, ISAAC 2022, Complete Volum