Highlights d Human P. copri isolates have diverse genomes making up four distinct clades d Genome diversity is exemplified by differences in susC genes and predicted PULs d P. copri isolates utilize distinct sets of plant polysaccharides
The gut-dwelling Prevotella copri, the most prevalent Prevotella species in human gut, have been associated with diet as well as disease, but our understanding of their diversity and functional roles remains rudimentary, as studies have been limited to 16S and metagenomic surveys and experiments using a single type strain. Here, we describe the genomic diversity of 83 P. copri isolates from 11 donors. We demonstrate that genomically distinct isolates, which can be categorized into different P. copri complex clades, utilize defined sets of plant polysaccharides that can be predicted in part from their genomes and from metagenomic data.This study thus reveals both genomic and functional differences in polysaccharide utilization between several novel human intestinal P. copri strains.
We produce combinatorial models for configuration space in a simplicial complex, and for configurations near a single point ("local configuration space.") The model for local configuration space is built out of the poset of poset structures on a finite set. The model for global configuration space relies on a combinatorial model for a simplicial complex with a deleted subcomplex. By way of application, we study the nodal curve y 2 z = x 3 + x 2 z, obtaining a presentation for its two-strand braid group, a conjectural presentation for its three-strand braid group, and presentations for its twoand three-strand local braid groups near the singular point.
The generators of the classical Specht module satisfy intricate relations. We introduce the Specht matroid, which keeps track of these relations, and the Specht polytope, which also keeps track of convexity relations. We establish basic facts about the Specht polytope, for example, that the symmetric group acts transitively on its vertices and irreducibly on its ambient real vector space. A similar construction builds a matroid and polytope for a tensor product of Specht modules, giving "Kronecker matroids" and "Kronecker polytopes" instead of the usual Kronecker coefficients. We dub this process of upgrading numbers to matroids and polytopes "matroidification," giving two more examples. In the course of describing these objects, we also give an elementary account of the construction of Specht modules different from the standard one. Finally, we provide code to compute with Specht matroids and their Chow rings.The irreducible representations of the symmetric group S n were worked out by Young and Specht in the early 20th century, and they remain omnipresent in algebraic combinatorics. The symmetric group S n has a unique irreducible representation for each partition of n. For example, S 4 has exactly five irreducible representations corresponding to the partitions (4) (
We study the end-behavior of integer-valued FI-modules. Our first result describes the high degrees of an FI-module in terms of newly defined tail invariants. Our main result provides an equivalence of categories between FI-tails and finitely supported modules for a new category that we call FJ. Objects of FJ are natural numbers, and morphisms are infinite series with summands drawn from certain modules of Lie brackets.
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