Kostant′s Conjecture Holds for E7: L2(37) <E7(C)
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چکیده
منابع مشابه
Dejean's conjecture holds for n>=30
We extend Carpi’s results by showing that Dejean’s conjecture holds for n ≥ 30. The following definitions are from sections 8 and 9 of [1]: Fix n ≥ 30. Let m = ⌊(n− 3)/6⌋. Let Am = {1, 2, . . . , m}. Let ker ψ = {v ∈ A ∗ m|∀a ∈ Am, 4 divides |v|a}. (In fact, this is not Carpi’s definition of ker ψ, but rather the assertion of his Lemma 9.1.) A word v ∈ A+m is a ψ-kernel repetition if it has per...
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The Komlós conjecture in discrepancy theory states that for some constant K and for any m× n matrix A whose columns lie in the unit ball there exists a vector x ∈ {−1,+1} such that ‖Ax‖∞ ≤ K. This conjecture also implies the Beck-Fiala conjecture on the discrepancy of bounded degree hypergraphs. Here we prove a natural relaxation of the Komlós conjecture: if the columns of A are assigned unit v...
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Hoàng-Reed conjecture asserts that every digraph D has a collection C of circuits C1, . . . , Cδ+ , where δ is the minimum outdegree of D, such that the circuits of C have a forest-like structure. Formally, |V (Ci) ∩ (V (C1) ∪ . . . ∪ V (Ci−1))| ≤ 1, for all i = 2, . . . , δ. We verify this conjecture for the class of tournaments.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1993
ISSN: 0021-8693
DOI: 10.1006/jabr.1993.1234