1,145 research outputs found
Disjoint finite partial steiner triple systems can be embedded in disjoint finite steiner triple systems
AbstractThis paper shows that a pair of disjoint finite partial Steiner triple systems can be embedded in a pair of disjoint finite Steiner triple systems
Complex Hadamard matrices of order 6: a four-parameter family
In this paper we construct a new, previously unknown four-parameter family of
complex Hadamard matrices of order 6, the entries of which are described by
algebraic functions of roots of various sextic polynomials. We conjecture that
the new, generic family G together with Karlsson's degenerate family K and
Tao's spectral matrix S form an exhaustive list of complex Hadamard matrices of
order 6. Such a complete characterization might finally lead to the solution of
the famous MUB-6 problem.Comment: 17 pages; Contribution to the workshop "Quantum Physics in higher
dimensional Hilbert Spaces", Traunkirchen, Austria, July 201
On the structure of phase transition maps for three or more coexisting phases
This paper is partly based on a lecture delivered by the author at the ERC
workshop "Geometric Partial Differential Equations" held in Pisa in September
2012. What is presented here is an expanded version of that lecture.Comment: 23 pages, 6 figure
Entropy in Dimension One
This paper completely classifies which numbers arise as the topological
entropy associated to postcritically finite self-maps of the unit interval.
Specifically, a positive real number h is the topological entropy of a
postcritically finite self-map of the unit interval if and only if exp(h) is an
algebraic integer that is at least as large as the absolute value of any of the
conjugates of exp(h); that is, if exp(h) is a weak Perron number. The
postcritically finite map may be chosen to be a polynomial all of whose
critical points are in the interval (0,1). This paper also proves that the weak
Perron numbers are precisely the numbers that arise as exp(h), where h is the
topological entropy associated to ergodic train track representatives of outer
automorphisms of a free group.Comment: 38 pages, 15 figures. This paper was completed by the author before
his death, and was uploaded by Dylan Thurston. A version including endnotes
by John Milnor will appear in the proceedings of the Banff conference on
Frontiers in Complex Dynamic
Embedding in a perfect code
A binary 1-error-correcting code can always be embedded in a 1-perfect code
of some larger lengthComment: Eng: 5pp, Rus: 5pp. V3: revised, a survey added; the accepted
version; Russian translation adde
Computing representations for radicals of finitely generated differential ideals
International audienceThis paper deals with systems of polynomial di erential equations, ordinary or with partial derivatives. The embedding theory is the di erential algebra of Ritt and Kolchin. We describe an algorithm, named Rosenfeld-Gröbner, which computes a representation for the radical p of the diff erential ideal generated by any such sys- tem . The computed representation constitutes a normal simpli er for the equivalence relation modulo p (it permits to test embership in p). It permits also to compute Taylor expansions of solutions of . The algorithm is implemented within a package in MAPLE
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