If p is a permutation of n digits, we define it's 'pattern' as follows: Begin at the left most digit, and make a list of the first numbers higher than this one, including this one. Move to the right-most digit, and make a list of the first numbers lower than this one. Move to the next available left digit, and repeat until the permutation is exhausted. For example, take 358926471. We begin 3589 - no number is higher than 9, so we can stop. Then 1. 2 is the next available left digit, so we write 26, and finally 74. So this permutation has the pattern: 3589 1 26 74. Another example; 87214536 becomes 8 631 7 542 This example is easy to see as not unique - e.g. 87245136 has the same pattern. Now for the questions: 1) Is there a combinatorial interpretation for a pattern? 2) Given a pattern, determine the number of permutations that fit it. Jon Perry perry@globalnet.co.uk http://www.users.globalnet.co.uk/~perry/maths/ http://www.users.globalnet.co.uk/~perry/DIVMenu/ BrainBench MVP for HTML and JavaScript http://www.brainbench.com