Euler Zigzag Numbers
Euler Zigzag Numbers
An alternating permutation is one in which the difference between each successive pair of adjacent elements changes sign—this is, each "rise" is followed by a "fall", and vice versa. For example, the permutation {1324} is an alternating permutation.
The number of alternating permutations on elements is sometimes called the Euler zigzag number.
n
Flipping the image upside-down with the "flip" control toggles between the alternating permutations that begin with a rise and those that begin with a fall.
External Links
External Links
Permanent Citation
Permanent Citation
Robert Dickau
"Euler Zigzag Numbers"
http://demonstrations.wolfram.com/EulerZigzagNumbers/
Wolfram Demonstrations Project
Published: March 25, 2008