2,2

A universal cycle of permutations is a cycle of n! digits such that each permutation of {1,...,n} occurs exactly once as a block of n-1 consecutive digits (with its redundant final element suppressed). a(4)=2^7*3, a(5)=2^33*3^8*5^3, a(6)=2^190*3^49*5^33, a(7)=2^1217*3^123*5^119*7^5*11^28*43^35*73^20*79^21*109^35 ~=1.582284037*10^747.

Brad Jackson, Universal cycles of k-subsets and k-permutations, Discrete Math. 117 (1993), no. 1-3, 141-150.

D. E. Knuth, The Art of Computer Programming, Volume 4, Fascicle 2, Generating All Tuples and Permutations. Ch. 7.2.1.2, Exercises 111 and 112, Page 75 and Answer to Exercise 112, pages 120-121.

(121323) is a universal cycle of permutations for n=3,

(123124132134214324314234) is one for n=4.

Sequence in context: A157577 A062604 A160192 this_sequence A137023 A152517 A087771

Adjacent sequences: A120058 A120059 A120060 this_sequence A120062 A120063 A120064

nonn

Hugo Pfoertner (hugo(AT)pfoertner.org), Jun 06 2006