1 citations · 1 across the 6 of their papers we have counts for
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Asymptotically sharp bounds for affine subspace statistics in
Ting-Wei Chao, Zixuan Xu, Dmitrii Zakharov
Given a subset , we can consider the distribution of the intersection size of with a uniformly random -flat . Motivated by the edge statistics…
Affine Subspace Statistics in the Hypercube
Zixuan Xu
We study the intersection statistics of affine subspaces in the hypercube , motivated by recent work of Alon, Axenovich, and Goldwasser on the intersection statisti…
Vertex-minor universality of a random graph
Ting-Wei Chao, Zixuan Xu
Given a graph and a vertex , a local complementation at on is an operation that replaces the induced graph on the neighborhood of by its complement. A gr…
Improved lower bound for hypercube edge slicing
Lisa Sauermann, Zixuan Xu
How many hyperplanes in are needed in order to slice every edge of the -dimensional hypercube with vertex set ? Here, we say that a hyperplane $H\sub…
Nondegenerate hyperplane covers of the hypercube
Lisa Sauermann, Zixuan Xu
We consider collections of hyperplanes in covering all vertices of the -dimensional hypercube , which satisfy the following nondegeneracy condition: Fo…
Even-degeneracy of a random graph
Ting-Wei Chao, Dingding Dong, Zixuan Xu
A graph is even-degenerate if one can iteratively remove a vertex of even degree at each step until at most one edge remains. Recently, Janzer and Yip showed that the Erdős--Renyi…
Essential covers of the hypercube require many hyperplanes
Lisa Sauermann, Zixuan Xu
We prove a new lower bound for the almost 20 year old problem of determining the smallest possible size of an essential cover of the -dimensional hypercube , i.e. t…