منابع مشابه
The Lax Conjecture Is True
In 1958 Lax conjectured that hyperbolic polynomials in three variables are determinants of linear combinations of three symmetric matrices. This conjecture is equivalent to a recent observation of Helton and Vinnikov. Consider a polynomial p on R of degree d (the maximum of the degrees of the monomials in the expansion of p). We call p homogeneous if p(tw) = tp(w) for all real t and vectors w ∈...
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In 1977 a five-part conjecturewasmade about a family of groups related to trivalent graphs and one part of the conjecture was proved. The conjecture completely determines all finite members of the family. Here we prove another part of the conjecture and foreshadow a paper which completes the proof of the other three parts.
متن کاملToida's Conjecture is True
Let S be a subset of the units in Zn. Let Γ be a circulant graph of order n (a Cayley graph of Zn) such that if ij ∈ E(Γ), then i − j (mod n) ∈ S. Toida conjectured that if Γ′ is another circulant graph of order n, then Γ and Γ′ are isomorphic if and only if they are isomorphic by a group automorphism of Zn. In this paper, we prove that Toida’s conjecture is true. We further prove that Toida’s ...
متن کاملThe Prime Power Conjecture is True for
The Prime Power Conjecture (PPC) states that abelian planar difference sets of order n exist only for n a prime power. Evans and Mann [1] verified this for cyclic difference sets for n ≤ 1600. In this paper we use the Mann test to verify the PPC for n ≤ 2, 000, 000.
متن کاملThe Strong Anick Conjecture Is True
Recently Umirbaev has proved the long-standing Anick conjecture, that is, there exist wild automorphisms of the free associative algebra K〈x, y, z〉 over a field K of characteristic 0. In particular, the well-known Anick automorphism is wild. In this article we obtain a stronger result (the Strong Anick Conjecture that implies the Anick Conjecture). Namely, we prove that there exist wild coordin...
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ژورنال
عنوان ژورنال: Journal of the ACM
سال: 2013
ISSN: 0004-5411,1557-735X
DOI: 10.1145/2487241.2487243