ar X iv : m at h / 06 06 45 1 v 1 [ m at h . C O ] 1 9 Ju n 20 06 TWO COLOR OFF - DIAGONAL RADO - TYPE NUMBERS
نویسنده
چکیده
We show that for any two linear homogenous equations E0, E1, each with at least three variables and coefficients not all the same sign, any 2-coloring of Z+ admits monochromatic solutions of color 0 to E0 or monochromatic solutions of color 1 to E1. We define the 2-color off-diagonal Rado number RR(E0, E1) to be the smallest N such that [1, N ] must admit such solutions. We determine a lower bound for RR(E0, E1) in certain cases when each Ei is of the form a1x1 + . . . + anxn = z as well as find the exact value of RR(E0, E1) when each is of the form x1 + a2x2 + . . . + anxn = z. We then present a Maple package that determines upper bounds for off-diagonal Rado numbers of a few particular types, and use it to quickly prove two previous results for diagonal Rado numbers.
منابع مشابه
ar X iv : m at h / 06 06 67 1 v 1 [ m at h . A C ] 2 7 Ju n 20 06 PRÜFER ⋆ – MULTIPLICATION DOMAINS AND ⋆ – COHERENCE
متن کامل
ar X iv : m at h / 06 06 33 9 v 1 [ m at h . SP ] 1 4 Ju n 20 06 Eigenfunction expansions associated with 1 d periodic differential operators of order 2 n
We prove an explicit formula for the spectral expansions in L(R) generated by selfadjoint differential operators (−1) d dx2n + n−1
متن کاملar X iv : m at h / 06 06 43 6 v 1 [ m at h . Q A ] 1 9 Ju n 20 06 NONCOMMUTATIVE POISSON STRUCTURES ON ORBIFOLDS
In this paper, we compute the Gerstenhaber bracket on the Hochschild cohomology of C∞(M)⋊Γ. Using this computation, we classify all the noncommutative Poisson structures on C∞(M) ⋊ Γ when M is a symplectic manifold. We provide examples of deformation quantizations of these noncommutative Poisson structures.
متن کاملar X iv : m at h / 05 06 37 9 v 1 [ m at h . G N ] 1 9 Ju n 20 05 Residuality of Families of F σ Sets Shingo
We prove that two natural definitions of residuality of families of Fσ sets are equivalent. We make use of the Banach-Mazur game in the proof.
متن کاملar X iv : m at h / 06 06 27 5 v 1 [ m at h . A T ] 1 2 Ju n 20 06 MODULES IN MONOIDAL MODEL CATEGORIES
This paper studies the existence of and compatibility between derived change of ring, balanced product, and function module derived functors on module categories in monoidal model categories.
متن کامل