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Abstract Let be a finite, connected graph. We consider a greedy selection of vertices: given a list of vertices , take to be any vertex maximizing the sum of distances to the vertices already chosen and iterate, keep adding the “most remote” vertex. The frequency with which the vertices of the graph appear in this sequence converges to a set of probability measures with nice properties. The support of these measures is, generically, given by a rather small number of vertices . We prove that this suggests that the graphGis, in a suitable sense, “m‐dimensional” by exhibiting an explicit 1‐Lipschitz embedding with good properties.
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On the vertex functions of type A quiver varieties
Abstract The goal of this paper is to better understand the quasimap vertex functions of typeANakajima quiver varieties. To that end, we construct an explicit embedding of any typeAquiver variety into a typeAquiver variety with all framings at the rightmost vertex of the quiver. Then, we consider quasimap counts, showing that the map induced by this embedding on equivariantK-theory preserves vertex functions.
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- Award ID(s):
- 1645877
- PAR ID:
- 10489024
- Publisher / Repository:
- Springer Science + Business Media
- Date Published:
- Journal Name:
- Letters in Mathematical Physics
- Volume:
- 114
- Issue:
- 1
- ISSN:
- 1573-0530
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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