The main results are as follows:( i ) For the number of chord diagrams of order n, an exact formula is given.( ii ) For the number of spine diagrams of order n, the upper and lower bounds are obtained. These bounds sh...The main results are as follows:( i ) For the number of chord diagrams of order n, an exact formula is given.( ii ) For the number of spine diagrams of order n, the upper and lower bounds are obtained. These bounds show that the estimation is asymptotically the best.As a byproduct, an upper bound is obtained, for the dimension of Vassiliev knot invariants of order n, that is, 1/2 ( n -1)! for any n≥3, and 1/2( n - 1)! - 1/2( n - 2)! for bigger n . Our upper bound is based on the work of Chmutov and Duzhin and is an improvement of their bound ( n - 1)! . For n = 3, and 4,1/2( n - 1)! is already the best.展开更多
文摘The main results are as follows:( i ) For the number of chord diagrams of order n, an exact formula is given.( ii ) For the number of spine diagrams of order n, the upper and lower bounds are obtained. These bounds show that the estimation is asymptotically the best.As a byproduct, an upper bound is obtained, for the dimension of Vassiliev knot invariants of order n, that is, 1/2 ( n -1)! for any n≥3, and 1/2( n - 1)! - 1/2( n - 2)! for bigger n . Our upper bound is based on the work of Chmutov and Duzhin and is an improvement of their bound ( n - 1)! . For n = 3, and 4,1/2( n - 1)! is already the best.
