Based on the kernel method, we present systematic methods to solve equation systems on generating functions of two variables. Using these methods, we get the generating functions for the number of permutations which avoid 1234 and 12 k (k - 1) ... 3 and permutations which avoid 1243 and 12 ... k.
Bibliographical noteFunding Information:
We thank Dr. G. Xin for many references. The second author is partially supported by a NKBRPC (2004CB318000), the Ministry of Education and the National Science Foundation of China.
- Forbidden subsequences
- Kernel method
- Restricted permutations
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics