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11 Oct 2006: "!#$%&(')( ,.-0/. 1 3246587:96;8<=5?>A@BDCFEGCIHKJL>A5JMNMPO6>AN;Q5R S6T:5U@3NVW5?XY5?>ZJLO6O 5?7[JYJN7VAZJLVWVAD>]5U57:96;8< 5>A@3T _VA65_aT>A;cbdAb ef GdAb e#gQJL>A5hJMMO6>AN;Q5ji. Gk-05?Vml05U5U7 1 hJ76SQ

18 Sep 2006: aj Aj and 1 r dj ;. • xα Tj {0} for all α; and. • ... whenever SAk1,Ak,. ,Aj (j 1) is k-coloured, we can find Aj1 Aj1and f : [dj ]. aAj1 [(a 1)dj1 1, adj1] Tj such that the set. SfAk1,Ak,.

2 Aug 2006: 5, ,h-x àÉ»kµ-!cfã j î X Z á ì ] ËÙy«Ô ãâhá ìØ Ô ãâ3ìØÔ ãâ¢áØaßɵ&ĵ(«Ô ãâhákØ j= - ùþ ËyÃīѵwÁ>Á Ë &µyÁBº«È Tj{ -

1 Jun 2006: Then Φ is an m m alternating matrix with each entryΦij either 0 or a non-constant homogeneous polynomial of degree s ti tj = (ri rj)/2 where ri = s2ti.

26 Apr 2006: r[oLztLrp3qYjwp.luq6sSOnvNrpxsO6sS6ypxrsS6v.S66nr[6oOn.j[6sO!yn?«!j[}6OnNtIr[|v.r}6!pxjwpxsSrYj[n?àãnNvNpxtNj[6luq6sSOnv.rpxsS6sO6ypxrj[6}sSpBpxq!nv.r!tLpxoL6vNp3sOr!tj[6vqYj[o3j[vNp3n.o3sStxjwp3sOr!tQr[|ãpxq6nWt36}Öj[ ... r[p|CroBn.6oLsOvq6nNpxq6nNr

10 Oct 2006: g(j)i = {x (nj , nj1] : x nj i tj (mod r2j )}. So in particular, we have. g(0)i = {1 x n r1 : x i (mod t)}.

6 Apr 2006: zi Tj for i dj. Now, by the pigeonhole principle, some two of the sets S0, S1,. , ... tdi Ti1} is. monochromatic;. • zi Tj for i dj.