Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Abstract    consider two versions of a game for two players,  A  and  B . The game consists of manipulations of words of length  n  over an alphabet of size σ, for arbitrary  n  and σ. For σ = 2 the game is described as follows: initially, player  A  puts  n  drinking glasses on a round table, some of which are upside down. Player  B  attempts to force player  A  to set all the glasses in the upright position. For this, he instructs player  A  to invert some of the glasses. Before following the instruction, player  A  has the freedom to rotate the table, and then to invert the glasses that are in the locations originally pointed by player  B . In one version of the game, player  B  is blindfolded and in the other he is not.  show that player  B  has winning strategies for both games iff  n  and σ are pors of the same prime. In both games  provide optimal winning strategies for  B .  The analysis of the games is closely related to the concept of the  derivative  of a σ-ary word of length  n . In particular, it is related to the  depth  of such word, which is the smallest  k  such that the  k th derivative of the word is the all-zero word.  give tight upper bounds on the depth of σ-ary words of length  n , where σ and  n  are pors of the same prime.
['Reuven Bar Yehuda', 'Tuvi Etzion', 'Shlomo Moran']
I am writing a research paper on a idea Rotating-table games and derivatives of words
[{"from": "human", "value": "I am writing a research paper on a idea Rotating-table games and derivatives of words"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Abstract    consider two versions of a game for two players,  A  and  B . The game consists of manipulations of words of length  n  over an alphabet of size \u03c3, for arbitrary  n  and \u03c3. For \u03c3 = 2 the game is described as follows: initially, player  A  puts  n  drinking glasses on a round table, some of which are upside down. Player  B  attempts to force player  A  to set all the glasses in the upright position. For this, he instructs player  A  to invert some of the glasses. Before following the instruction, player  A  has the freedom to rotate the table, and then to invert the glasses that are in the locations originally pointed by player  B . In one version of the game, player  B  is blindfolded and in the other he is not.  show that player  B  has winning strategies for both games iff  n  and \u03c3 are pors of the same prime. In both games  provide optimal winning strategies for  B .  The analysis of the games is closely related to the concept of the  derivative  of a \u03c3-ary word of length  n . In particular, it is related to the  depth  of such word, which is the smallest  k  such that the  k th derivative of the word is the all-zero word.  give tight upper bounds on the depth of \u03c3-ary words of length  n , where \u03c3 and  n  are pors of the same prime."}]