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Earth-Science Reviews, 2022 The diversification of animals during the Cambrian Period is one of the most significant evolutionary events in Earth ’ s history. However, the sequence of events leading to the origin of ‘modern ’ ecosystems and the exact temporal relationship between ...
T. Topper +7 more
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Calibrating the temporal and spatial dynamics of the Ediacaran - Cambrian radiation of animals
Earth-Science Reviews, 2021 The Ediacaran-Cambrian transition, which incorporates the radiation of animals, lacks a robust global temporal and spatial framework, resulting in major uncertainty in the evolutionary dynamics of this critical radiation and its relationship to changes ...
F. Bowyer +9 more
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Sublattices of associahedra and permutohedra [PDF]
Advances in Applied Mathematics, 2011 Gratzer asked in 1971 for a characterization of sublattices of Tamari lattices. A natural candidate was coined by McKenzie in 1972 with the notion of a bounded homomorphic image of a free lattice-in short, bounded lattice.
L. Santocanale, F. Wehrung
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Current understanding on the Cambrian Explosion: questions and answers
PalZ, 2021 The Cambrian Explosion by nature is a three-phased explosion of animal body plans alongside episodic biomineralization, pulsed change of generic diversity, body size variation, and progressive increase of ecosystem complexity.
Xingliang Zhang, D. Shu
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Fossil evidence unveils an early Cambrian origin for Bryozoa
Nature, 2021 Bryozoans (also known as ectoprocts or moss animals) are aquatic, dominantly sessile, filter-feeding lophophorates that construct an organic or calcareous modular colonial (clonal) exoskeleton1–3.
Zhiliang Zhang +9 more
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The extended permutohedron on a transitive binary relation [PDF]
, 2013 For a given transitive binary relation e on a set E, the transitive closures of open (i.e., co-transitive in e) sets, called the regular closed subsets, form an ortholattice Reg(e), the extended permutohedron on e.
Santocanale, Luigi, Wehrung, Friedrich
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EL-labelings and canonical spanning trees for subword complexes [PDF]
, 2012 We describe edge labelings of the increasing flip graph of a subword complex on a finite Coxeter group, and study applications thereof. On the one hand, we show that they provide canonical spanning trees of the facet-ridge graph of the subword complex ...
Vincent Pilaud, Christian Stump
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The facial weak order and its lattice quotients [PDF]
, 2016 We investigate a poset structure that extends the weak order on a finite Coxeter group $W$ to the set of all faces of the permutahedron of $W$. We call this order the facial weak order.
Dermenjian, Aram +2 more
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Lattice theory of torsion classes [PDF]
, 2018 The aim of this paper is to establish a lattice theoretical framework to study the partially ordered set $\operatorname{\mathsf{tors}} A$ of torsion classes over a finite-dimensional algebra $A$.
Demonet, Laurent +4 more
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Oriented flip graphs of polygonal subdivisions and noncrossing tree partitions
Journal of Combinatorial Theory, 2018 Given a tree embedded in a disk, we introduce a simplicial complex of noncrossing geodesics supported by the tree, which we call the noncrossing complex. The facets of the noncrossing complex have the structure of an oriented flip graph. Special cases of
Alexander Garver, T. McConville
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