9. Kernel Method and systems of functional equations with several conditions(2007, University of Haifa and Nankai University) We generalize the kernel method to equation systems in which the numbers of unknowns are allowed to exceed the numbers of equations. With this generalization, we work out the generating functions for several types of sequences and generating trees whose recursions are dependent on the parity of the indices.

8. Restricted Partitions of [n]={1,2,...,n}(2007, University of Haifa). Here we give two programs: (1) For given n the first program gives the list of all partitions of [n]. (2) For given a list of patterns and level n the second program gives the number of partitions of [n] that avoid each pattern in the input list.

7. Signed Permutations(2007, University of Haifa). Here we give two programs: (1) for given a pattern of length 3,4 or 5 and a positive integer k the program find the number of signed permutations of length n that avoid the pattern, for n=1,2,...,k. (2) The second program classifies the classes of patterns of length 5 up to symmetry and Theorem 2.1 (as described in the corresponding paper). Note that the second program gives at the end 160 classes, to reduce this number to 137 you need to classify the equivalences classes using the classification of permutation of length 5 (the classical case of S_5), as described in the corresponding paper. Also, we note that the first program used to find the corresponding sequence for each class.

6. Kernel Method and Linear Recurrence System(2006, University of Haifa and Nankai University) Based on the kernel method, we present systematic methods, called

5. Counting occurrences of the pattern 231 in an involution(2004, University of Haifa, Nankai University) Our Program finds an equation that present a formula of the generating function for the number of involutions on n letters which contain the pattern 231 exactly r times. The program running with input r and its output is an equation for I_r(x) (see the output file). This equation can be solved by using Maple where the expressions of I_j(x), j=0,1,...,r-1, are given.

4. Finite Automata and pattern avoidance(2003, University of Haifa) Our Program for finding a formula for |[k]^n(p)| (M_{n,m}^k(p) the number of matrices with n columns , m rows, on k letters which avoid the pattern p, [k]^n(p)=M_{n,1}^k(p)) is

3. pawns.mws and pawns_kings.mws(2003, Chalmers Institute of Technology) This program supports the paper

2. genmu.mws and findav.mws(2003, Chalmers Institute of Technology) These two programs support the paper

1. avoid132.mws(2001, University of Haifa) This program supports the paper