Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In 1984 T. Carlson and S. Simpson established an infinitary extension of the Hales–Jett Theorem in which the leftmost letters of all but one of the words re required to be variables. ( call such words left variable words.)   extend the Carlson–Simpson result for left variable words, prove a corresponding result about right variable words, and determine precisely the extent to which left and right variable words can be combined in such extensions. The results mentioned so far all involve a finite alphabet.  show that the results for left variable words do not extend to words over an infinite alphabet, but that the results for right variable words do extend.
['Neil Hindman', 'Randall McCutcheon']
I am writing a research paper on a idea Partition Theorems for Left and Right Variable Words
[{"from": "human", "value": "I am writing a research paper on a idea Partition Theorems for Left and Right Variable Words"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In 1984 T. Carlson and S. Simpson established an infinitary extension of the Hales\u2013Jett Theorem in which the leftmost letters of all but one of the words re required to be variables. ( call such words left variable words.)   extend the Carlson\u2013Simpson result for left variable words, prove a corresponding result about right variable words, and determine precisely the extent to which left and right variable words can be combined in such extensions. The results mentioned so far all involve a finite alphabet.  show that the results for left variable words do not extend to words over an infinite alphabet, but that the results for right variable words do extend."}]