Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Abstract   In this issue, W.J. Walker introduces the lattice  L(n, r)  as the set of all possible results when  n  competitors are matched in a series of  r  races. A result is an  r -term nondecreasing sequence of integers selected from {1,2,…, n }. The dimension of  L(n, r)  is at most  r  since it is a subposet of   R     t   . Walker conjectures that  L(n, r)  is at fact the intersection of  r  consistent linear extensions and verifies this conjecture when  r  ⩽ 2 as ll as for the case ( n ,  r ) = (4, 3). In this note,  show that the general conjecture does not hold by providing that for every  r  >/ 3 and every  t  ⩾  r , there exists an integer  n  0  so that if  n  ⩾ n 0 , then  L(n, r)  is not the intersection of  t  consistent linear extensions.
['Vojtech Rödl', 'William T. Trotter']
I am writing a research paper on a idea A note on ranking functions
[{"from": "human", "value": "I am writing a research paper on a idea A note on ranking functions"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Abstract   In this issue, W.J. Walker introduces the lattice  L(n, r)  as the set of all possible results when  n  competitors are matched in a series of  r  races. A result is an  r -term nondecreasing sequence of integers selected from {1,2,\u2026, n }. The dimension of  L(n, r)  is at most  r  since it is a subposet of   R     t   . Walker conjectures that  L(n, r)  is at fact the intersection of  r  consistent linear extensions and verifies this conjecture when  r  \u2a7d 2 as ll as for the case ( n ,  r ) = (4, 3). In this note,  show that the general conjecture does not hold by providing that for every  r  >/ 3 and every  t  \u2a7e  r , there exists an integer  n  0  so that if  n  \u2a7e n 0 , then  L(n, r)  is not the intersection of  t  consistent linear extensions."}]