“Extra” step in counting the number of ways to have a domino tiling of a 4 by n rectangle?
The picture above explains a method for doing this via generating functions & finite state machines, but what I do not get is why we must record the number of dominoes used to make a state transition. Why does the number of transitions alone suffice? Why is it that we need $mt^b$ to record a transition instead of just $m$?
combinatorics generating-functions tiling transition-matrix
asked Dec 8 at 9:04
Saad
570211
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The picture above explains a method for doing this via generating functions & finite state machines, but what I do not get is why we must record the number of dominoes used to make a state transition. Why does the number of transitions alone suffice? Why is it that we need $mt^b$ to record a transition instead of just $m$?
combinatorics generating-functions tiling transition-matrix
asked Dec 8 at 9:04
Saad
570211
add a comment |
The picture above explains a method for doing this via generating functions & finite state machines, but what I do not get is why we must record the number of dominoes used to make a state transition. Why does the number of transitions alone suffice? Why is it that we need $mt^b$ to record a transition instead of just $m$?
combinatorics generating-functions tiling transition-matrix
asked Dec 8 at 9:04
Saad
570211
The picture above explains a method for doing this via generating functions & finite state machines, but what I do not get is why we must record the number of dominoes used to make a state transition. Why does the number of transitions alone suffice? Why is it that we need $mt^b$ to record a transition instead of just $m$?
combinatorics generating-functions tiling transition-matrix
combinatorics generating-functions tiling transition-matrix
asked Dec 8 at 9:04
Saad
570211
asked Dec 8 at 9:04
Saad
570211
asked Dec 8 at 9:04
Saad
570211
asked Dec 8 at 9:04
Saad
570211
asked Dec 8 at 9:04
Saad
570211
570211
add a comment |
add a comment |
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