AbstractFor a family of subsets S of a finite set V, a coloring χ:V→{-1,1}, and Sj∈S, let χ(Sj)=∑v∈Sjχ(v). We consider the problem to minimize ∑jχ(Sj)2 and we call the problem L2-discrepancy problem. We show that the problem is NP-complete, and we also provide an upper bound for the L2-discrepancy
AbstractLet H be a hypergraph. For a k-edge coloring c:E(H)→{1,…,k} let f(H,c) be the number of comp...
AbstractThiémard (J. Complexity 17(4) (2001) 850) suspects that his upper bound for the discrepancy ...
AbstractGiven Mikhlin–Hörmander multipliers mi,i=1,…,N, with uniform estimates we prove an optimal l...
AbstractA cutset in the poset 2[n], of subsets of {1, …, n} ordered by inclusion, is a subset of 2[n...
Consider a set $X\subseteq \mathbb{R}^d$ which is 1-dense, namely, it intersects every unit ball. We...
AbstractI prove that in a tree in which the distance between any two endpoints is even, there is a m...
AbstractK. F. Roth (1964, Acta. Arith.9, 257–260) proved that the discrepancy of arithmetic progress...
AbstractLet m(n,k,r,t) be the maximum size of F⊂[n]k satisfying |F1∩⋯∩Fr|≥t for all F1,…,Fr∈F. We pr...
In this paper, we establish Schr\"{o}dinger maximal estimates associated with the finite type phases...
AbstractLet fr(n) be the maximum number of edges in an r-uniform hypergraph on n vertices that does ...
AbstractFor positive integers m and r, one can easily show there exist integers N such that for ever...
AbstractLet t≥26 and let ℱ be a k-uniform hypergraph on n vertices. Suppose that |F1∩F2∩F3|≥t holds ...
AbstractThe linear discrepancy problem is to round a given [0,1]-vector x to a binary vector y such ...
AbstractFor a family of subsets S of a finite set V, a coloring χ:V→{-1,1}, and Sj∈S, let χ(Sj)=∑v∈S...
AbstractThe maximum number of edges spanned by a subset of given diameter in a Hamming space with al...
AbstractLet H be a hypergraph. For a k-edge coloring c:E(H)→{1,…,k} let f(H,c) be the number of comp...
AbstractThiémard (J. Complexity 17(4) (2001) 850) suspects that his upper bound for the discrepancy ...
AbstractGiven Mikhlin–Hörmander multipliers mi,i=1,…,N, with uniform estimates we prove an optimal l...
AbstractA cutset in the poset 2[n], of subsets of {1, …, n} ordered by inclusion, is a subset of 2[n...
Consider a set $X\subseteq \mathbb{R}^d$ which is 1-dense, namely, it intersects every unit ball. We...
AbstractI prove that in a tree in which the distance between any two endpoints is even, there is a m...
AbstractK. F. Roth (1964, Acta. Arith.9, 257–260) proved that the discrepancy of arithmetic progress...
AbstractLet m(n,k,r,t) be the maximum size of F⊂[n]k satisfying |F1∩⋯∩Fr|≥t for all F1,…,Fr∈F. We pr...
In this paper, we establish Schr\"{o}dinger maximal estimates associated with the finite type phases...
AbstractLet fr(n) be the maximum number of edges in an r-uniform hypergraph on n vertices that does ...
AbstractFor positive integers m and r, one can easily show there exist integers N such that for ever...
AbstractLet t≥26 and let ℱ be a k-uniform hypergraph on n vertices. Suppose that |F1∩F2∩F3|≥t holds ...
AbstractThe linear discrepancy problem is to round a given [0,1]-vector x to a binary vector y such ...
AbstractFor a family of subsets S of a finite set V, a coloring χ:V→{-1,1}, and Sj∈S, let χ(Sj)=∑v∈S...
AbstractThe maximum number of edges spanned by a subset of given diameter in a Hamming space with al...
AbstractLet H be a hypergraph. For a k-edge coloring c:E(H)→{1,…,k} let f(H,c) be the number of comp...
AbstractThiémard (J. Complexity 17(4) (2001) 850) suspects that his upper bound for the discrepancy ...
AbstractGiven Mikhlin–Hörmander multipliers mi,i=1,…,N, with uniform estimates we prove an optimal l...
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