Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » Math Topics » discretemath

Topic: who can help me?friends.
Replies: 0  

Advanced Search

Back to Topic List Back to Topic List  
China -->hk

Posts: 43
Registered: 1/23/07
who can help me?friends.
Posted: Oct 16, 2007 3:08 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

question 1: there are n numbers:1,2,...,n^2.now arrange them in a nxn matrix such that each row and each is increasing.Then what is the permutation number?
As we know
(from http://www.research.att.com/~njas/sequences/?q=matrix+increasing+in+rows+and+columns&language=english)
the formula is
T(m, n) = 0!*1!*..*(n-1)! *(m*n)! / ( m!*(m+1)!*..*(m+n-1)! )
But can some respectful friend tell me how can we using high school knowledge(such as recurrence relation etc.,not using group)to deduce it out?If could,we can teach it in high school class.
question 2: if there an^3 numbers: 1,2,3,...,n^2,...,n^3,now arrange them in a cube (space) such that each row(x-axis),each column(y-axis) and each vertical line(z-axis) are strictly increasing,then what is the formula?
Thanks advancely,



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.