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Re: Super-Increasing List

  • To: mathgroup at smc.vnet.net
  • Subject: [mg40487] Re: Super-Increasing List
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Mon, 7 Apr 2003 04:56:53 -0400 (EDT)
  • Organization: Universitaet Leipzig
  • References: <b6m04c$efg$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

GreaterSumQ[{a_, b_}] := a < b
GreaterSumQ[{a__, b_}] := Plus[a] < b && GreaterSumQ[{a}]

SuperIncreasingQ[lst_] :=
   And @@ Less @@@ Partition[lst, 2, 1] && GreaterSumQ[lst]

Regards
  Jens

flip wrote:
> 
> Hello,
> 
> does a command or module exist which can test a list of values and determine
> if it is a super-increasing list?
> 
> A super-increasing list satifies the conditions:
> 
> a.  the list is in increasing order
> b.  each element of the list is greater than the sum of it's previous
> elements
> 
> Example:
> 
> list = {2, 3, 7, 15, 31}
> 
> So check:
> 
> a.  It is in  increasing order and
> b.   3 > 2, 7 > 3+ 2, 15 > 7 + 3 + 2 and 31 > 15 + 7 + 3 + 2,
> 
> hence the list is super-increasing.
> 
> Thanks for any inputs, Flip
> 
> To email me, remove "_alpha".


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