... γ be the 2-coloring of [1, N − 1] defined as follows. The first 2
q+1
2
− 1 integers
alternate colors with the color of 1 being blue. We then color
2
q+1
2
, 2q + 1
red. We
color the last ... not all the same sign, any 2-coloring of Z
+
admits
monochromatic solutions of color 0 to E
0
or monochromatic solutions of color 1 to E
1
.
We define the 2 -color off-diagonal Rado num...
... present result, analogously to the constructions of [6] and [1], can be
generalized to more than one color.
1
the electronic journal of combinatorics 7 (2000), #R15 3
Proof: We may assume that A is
... Rothschild ([GLR]).
Theorem 1.3 Let r, n, t ∈ N. There exists N = N (r, n, t) such that for any r-coloring
of the n-spaces of A
N
there exists a t-space V such that the family of n-spaces contained
in ... words, the function γ restricted to the standard n
2
-variable submatrices of v is
the lift of an r-coloring γ
of the set
F({1, ,L})
n
<
. By the choice of L, there thus
exist non-e...
... special case of a colored word is a colored permutation. A colored permutation is a
colored word in which each letter (either barred or unbarred) is used no more than once.
If w is a colored word, ... insertion. A doubly colored
biword w is called upper colored if w
inv
is a colored biword. That is, w has colors only
on the upper word. Left-right insertion is defined on upper colored biwords....