Inequalities or histogram or something.......
- To: mathgroup at smc.vnet.net
- Subject: [mg89338] Inequalities or histogram or something.......
- From: Steve Gray <stevebg at roadrunner.com>
- Date: Fri, 6 Jun 2008 06:47:03 -0400 (EDT)
Can Mathematica help with this? Or can someone? I have positive integers x1,x2,x3,k,v. There are assumptions: 1 <= k < v and 1 <= x1 < x2 < x3 <= v. There is one equation: k = x1 + x3 - x2 - 2. I need a symbolic solution for the number of combinations of x1,x2,x3 that satisfy the equation under the assumptions. This will be a histogram of k vs. the number of solutions. One numeric point on the histo: if v=8 and k=0, there are 6 solutions, x1,x2,x3 = 1,2,3; 1,3,4; 1,4,5; 1,5,6; 1,6,7; 1,7,8; none with x1 > 1. I need a general symbolic solution in terms of D(v,k). I need a way to show its derivation for a paper. I happen to know that D(v,k) + D(v,v-k-3) = 2(k+1)(v-k-2). This is not overwhelmingly complicated but I don't know a decent way to go about it. Thank you for any help, using Mathematica or not. (I have version 6.) Steve Gray