Results 1 to 10 of about 75,496 (347)
Adv. Math. 205 (2006), no. 2, 313-353., 2004 For an arbitrary finite Coxeter group W we define the family of Cambrian lattices for W as quotients of the weak order on W with respect to certain lattice congruences. We associate to each Cambrian lattice a complete fan, which we conjecture is the normal fan of a polytope combinatorially isomorphic to the generalized associahedron for W.
Reading, Nathan
arxiv +7 more sources
On the Topology of the Cambrian Semilattices [PDF]
The Electronic Journal of Combinatorics 20, 2 (2013) P48, 2012 For an arbitrary Coxeter group $W$, David Speyer and Nathan Reading defined Cambrian semilattices $C_{\gamma}$ as semilattice quotients of the weak order on $W$ induced by certain semilattice homomorphisms. In this article, we define an edge-labeling using the realization of Cambrian semilattices in terms of $\gamma$-sortable elements, and show that ...
Kallipoliti, Myrto, Mühle, Henri
arxiv +13 more sources
On the wildness of cambrian lattices [PDF]
arXiv, 2017 In this note, we investigate the representation type of the cambrian lattices and some other related lattices. The result is expressed as a very simple trichotomy. When the rank of the underlined Coxeter group is at most 2, the lattices are of finite representation type.
Chapoton, Frédéric, Rognerud, Baptiste
arxiv +7 more sources
Adv. Math., 311:598-633, 2017, 2014 Cambrian trees are oriented and labeled trees which fulfill local conditions around each node generalizing the conditions for classical binary search trees. Based on the bijective correspondence between signed permutations and leveled Cambrian trees, we define the Cambrian Hopf algebra generalizing J.-L. Loday and M. Ronco's algebra on binary trees. We
Chatel, Grégory, Pilaud, Vincent
arxiv +7 more sources
The C-value enigma and timing of the Cambrian explosion [PDF]
Biochemical and Biophysical Research Communications 392, 240-245
(2010), 2008 The Cambrian explosion is a grand challenge to science today and involves multidisciplinary study. This event is generally believed as a result of genetic innovations, environmental factors and ecological interactions, even though there are many conflicts on nature and timing of metazoan origins.
Adami +29 more
arxiv +3 more sources
The problem of the pre-Cambrian [PDF]
Geological Society of America Bulletin, 1908 Introduction Following the precedent of many scientific presidential addresses, I shall give a general review of one of the subjects which has occupied much of my time—the problem of the pre-Cambrian. Within an hour I can not consider the merits of the questions still in controversy, nor broadly cover the field mentioned; therefore I shall confine my ...
C. R. Van Hise
openalex +5 more sources
Adaptive walks in a gene network model of morphogenesis: insights into the Cambrian explosion [PDF]
arXiv, 2003 The emergence of complex patterns of organization close to the Cambrian boundary is known to have happened over a (geologically) short period of time. It involved the rapid diversification of body plans and stands as one of the major transitions in evolution. How it took place is a controversial issue.
Fernandez, Pau +2 more
arxiv +3 more sources
An analogue of distributivity for ungraded lattices [PDF]
arXiv, 2005 In this paper, we define a property, trimness, for lattices. Trimness is a not-necessarily-graded generalization of distributivity; in particular, if a lattice is trim and graded, it is distributive. Trimness is preserved under taking intervals and suitable sublattices. Trim lattices satisfy a weakened form of modularity.
Thomas, Hugh
arxiv +6 more sources
Cambrian triangulations and their tropical realizations [PDF]
European J. Combin., 83, 19 pp., 2020, 2018 This paper develops a Cambrian extension of the work of C. Ceballos, A. Padrol and C. Sarmiento on $\nu$-Tamari lattices and their tropical realizations. For any signature $\varepsilon \in \{\pm\}^n$, we consider a family of $\varepsilon$-trees in bijection with the triangulations of the $\varepsilon$-polygon.
Pilaud, Vincent
arxiv +3 more sources