Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  introduce a permutation analogue of the celebrated Szemeredi Regularity Lemma, and derive a number of consequences.  This tool allows us to provide a structural description of permutations which avoid a specified pattern, a result that permutations which scatter small intervals contain all possible patterns of a given size, a proof that every permutation avoiding a specified pattern has a nearly monotone linear-sized subset, and a "thin deletion" result.   also show how one can count sub-patterns of a permutation with an integral, and relate our results to permutation quasirandomness in a manner analogous to the graph-theoretic setting.
['Joshua N. Cooper']
I am writing a research paper on a idea A Permutation Regularity Lemma
[{"from": "human", "value": "I am writing a research paper on a idea A Permutation Regularity Lemma"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  introduce a permutation analogue of the celebrated Szemeredi Regularity Lemma, and derive a number of consequences.  This tool allows us to provide a structural description of permutations which avoid a specified pattern, a result that permutations which scatter small intervals contain all possible patterns of a given size, a proof that every permutation avoiding a specified pattern has a nearly monotone linear-sized subset, and a \"thin deletion\" result.   also show how one can count sub-patterns of a permutation with an integral, and relate our results to permutation quasirandomness in a manner analogous to the graph-theoretic setting."}]