Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider the problem of counting the set of Da,b of Dyck paths inscribed in ar ectangle of sizea × b. They are a natural general- ization of the classical Dyck words enumerated by the Catalan numbers. By using Ferrers diagrams associated to Dyck paths,  derive formulas for the enumeration of Da,b with a and b non relatively prime, in terms of Catalan numbers.
['Jose Eduardo Blazek']
I am writing a research paper on a idea New Formulas for Dyck Paths in a Rectangle
[{"from": "human", "value": "I am writing a research paper on a idea New Formulas for Dyck Paths in a Rectangle"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider the problem of counting the set of Da,b of Dyck paths inscribed in ar ectangle of sizea \u00d7 b. They are a natural general- ization of the classical Dyck words enumerated by the Catalan numbers. By using Ferrers diagrams associated to Dyck paths,  derive formulas for the enumeration of Da,b with a and b non relatively prime, in terms of Catalan numbers."}]