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I. P. GOULDEN, D. M. JACKSON AND R. VAKILConjecture. The approach is through the Ekedahl-Lando-Shapiro-Vainshtein theorem, which establishes the \polynomiality" of Hurwitz numbers, from which we pick...
I. P. GOULDEN, D. M. JACKSON AND R. VAKILConjecture. The approach is through the Ekedahl-Lando-Shapiro-Vainshtein theorem, which establishes the \polynomiality" of Hurwitz numbers, from which we pick...
Every submartingale S of class D has a unique Doob-Meyer decomposition S = M + A, where M is a martingale and A is a predictable increasing process starting at 0.
A standard Hilbert-space proof of Dirichlet’s principle is simplified, using an observation that a certain form of min-problem has unique solution, at a specified point. This solves Dirichlet’s proble...
We give an elementary proof of the Kontsevich conjecture that asserts that the iterations of the noncommutative rational map K_r:(x,y)-->(xyx^{-1},(1+y^r)x^{-1}) are given by noncommutative Laurent po...
Let K be a field and let m0, ...,mn be an almost arithmetic sequence of positive integers. Let C be a toric variety in the affine (n + 1)-space,defined parametrically by x0 = tm0 , . . . , xn = tmn. I...

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