Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In this note  give upper bounds for the number of vertices of the polyhedron P(A,b) = {x ∈ Rd: Ax < b} when the m × d constraint matrix A is subjected to certain restriction. For instance, if A is a 0/1-matrix, then there can be at most d! vertices and this bound is tight, or if the entries of A are non-negative integers so that each row sums to at most C, then there can be at most Cd vertices. These bounds are consequences of a more general theorem that the number of vertices of P(A,b) is at most d! ċ W/D, where W is the volume of the convex hull of the zero vector and the row vectors of A, and D is the smallest absolute value of any non-zero d × d subdeterminant of A.
['Khaled M. Elbassioni', 'Zvi Lotker', 'Raimund Seidel']
I am writing a research paper on a idea Upper bound on the number of vertices of polyhedra with 0, 1-constraint matrices
[{"from": "human", "value": "I am writing a research paper on a idea Upper bound on the number of vertices of polyhedra with 0, 1-constraint matrices"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In this note  give upper bounds for the number of vertices of the polyhedron P(A,b) = {x \u2208 Rd: Ax < b} when the m \u00d7 d constraint matrix A is subjected to certain restriction. For instance, if A is a 0/1-matrix, then there can be at most d! vertices and this bound is tight, or if the entries of A are non-negative integers so that each row sums to at most C, then there can be at most Cd vertices. These bounds are consequences of a more general theorem that the number of vertices of P(A,b) is at most d! \u010b W/D, where W is the volume of the convex hull of the zero vector and the row vectors of A, and D is the smallest absolute value of any non-zero d \u00d7 d subdeterminant of A."}]