6,692 research outputs found
Beyond topological persistence: Starting from networks
Persistent homology enables fast and computable comparison of topological
objects. However, it is naturally limited to the analysis of topological
spaces. We extend the theory of persistence, by guaranteeing robustness and
computability to significant data types as simple graphs and quivers. We focus
on categorical persistence functions that allow us to study in full generality
strong kinds of connectedness such as clique communities, -vertex and
-edge connectedness directly on simple graphs and monic coherent categories.Comment: arXiv admin note: text overlap with arXiv:1707.0967
On representing some lattices as lattices of intermediate subfactors of finite index
We prove that the very simple lattices which consist of a largest, a smallest
and pairwise incomparable elements where is a positive integer can be
realized as the lattices of intermediate subfactors of finite index and finite
depth. Using the same techniques, we give a necessary and sufficient condition
for subfactors coming from Loop groups of type at generic levels to be
maximal.Comment: 39 pages, latex, corrected proof of Cor. 5.23. To appear in Advance
in Mathematic
Order Quasisymmetric Functions Distinguish Rooted Trees
Richard P. Stanley conjectured that finite trees can be distinguished by
their chromatic symmetric functions. In this paper, we prove an analogous
statement for posets: Finite rooted trees can be distinguished by their order
quasisymmetric functions.Comment: 16 pages, 5 figures, referees' suggestions incorporate
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