New Ramsey Classes from Old

Let C_1 and C_2 be strong amalgamation classes of finite structures, with disjoint finite signatures sigma and tau. Then C_1 wedge C_2 denotes the class of all finite (sigma cup tau)-structures whose sigma-reduct is from C_1 and whose tau-reduct is from C_2. We prove that when C_1 and C_2 are Ramsey, then C_1 wedge C_2 is also Ramsey. We also discuss variations of this statement, and give several examples of new Ramsey classes derived from those general results.Comment: 11 pages. In the second version, to be submitted for journal publication, a number of typos has been removed, and a grant acknowledgement has been adde

Ramsey Properties of Permutations

The age of each countable homogeneous permutation forms a Ramsey class. Thus, there are five countably infinite Ramsey classes of permutations.Comment: 10 pages, 3 figures; v2: updated info on related work + some other minor enhancements (Dec 21, 2012

The origin of the Japanese and Korean accent systems

S.R. Ramsey writes (1979: 162): "The patterning of tone marks in Old Kyoto texts divides the vocabulary into virtually the same classes as those arrived at by comparing the accent distinctions found in the modern dialects. This means that the Old Kyoto dialect had a pitch system similar to that of proto-Japanese. The standard language of the Heian period may not actually be the ancestor of all the dialects of Japan, but at least as far as the accent system is concerned, it is close enough to the proto system to be used as a working model. The significance of this fact is important: It means that each of the dialects included in the comparison has as much to tell, at least potentially, as any other dialect about Old Kyoto accent.

Spartan Daily, August 29, 2006

Volume 127, Issue 3https://scholarworks.sjsu.edu/spartandaily/10261/thumbnail.jp

Large stars with few colors

A recent question in generalized Ramsey theory is that for fixed positive integers $s\leq t$, at least how many vertices can be covered by the vertices of no more than $s$ monochromatic members of the family $\cal F$ in every edge coloring of $K_n$ with $t$ colors. This is related to an old problem of Chung and Liu: for graph $G$ and integers $1\leq s<t$ what is the smallest positive integer $n=R_{s,t}(G)$ such that every coloring of the edges of $K_n$ with $t$ colors contains a copy of $G$ with at most $s$ colors. We answer this question when $G$ is a star and $s$ is either $t-1$ or $t-2$ generalizing the well-known result of Burr and Roberts

A Folkman Linear Family

For graphs $F$ and $G$, let $F\to (G,G)$ signify that any red/blue edge coloring of $F$ contains a monochromatic $G$. Define Folkman number $f(G;p)$ to be the smallest order of a graph $F$ such that $F\to (G,G)$ and $\omega(F) \le p$. It is shown that $f(G;p)\le cn$ for graphs $G$ of order $n$ with $\Delta(G)\le \Delta$, where $\Delta\ge 3$, $c=c(\Delta)$ and $p=p(\Delta)$ are positive constants.Comment: 11 page