Four-discordant permutations
Earl Glen Whitehead · Journal of the Australian Mathematical Society · 1979
Abstract A permutation π of the set {1, 2, …, n } is four-discordant if π( i ) ≢ i , i + 1, i + 2, i +3 (mod n ) for 1 ≦ i ≦ n . Generating functions for rook polynomials associated with four-discordant permutations are derived. Hit polynomials associated with four-discordant permutations are studied. Finally, it is shown that the leading coefficients of these rook polynomials form a “tribonacci” sequence which is a generalized Fibonacci sequence.