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- W2962934834 abstract "We study the rank of a random n × m matrix An,m;k with entries from GF(2), and exactly k unit entries in each column, the other entries being zero. The columns are chosen independently and uniformly at random from the set of all (nk) such columns.We obtain an asymptotically correct estimate for the rank as a function of the number of columns m in terms of c, n, k, and where m = cn/k. The matrix An,m;k forms the vertex-edge incidence matrix of a k-uniform random hypergraph H. The rank of An,m;k can be expressed as follows. Let |C2| be the number of vertices of the 2-core of H, and |E(C2)| the number of edges. Let m* be the value of m for which |C2| = |E(C2)|. Then w.h.p. for m" @default.
- W2962934834 created "2019-07-30" @default.
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- W2962934834 date "2019-01-06" @default.
- W2962934834 modified "2023-09-23" @default.
- W2962934834 title "On the rank of a random binary matrix" @default.
- W2962934834 doi "https://doi.org/10.5555/3310435.3310493" @default.
- W2962934834 hasPublicationYear "2019" @default.
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