OFFSET
1,4
COMMENTS
A small descent in a permutation p is a position i such that p(i)-p(i+1)=1.
A strong fixed point is a fixed point (or splitter) p(k)=k such that p(i) < k for i < k and p(j) > k for j > k.
REFERENCES
E. R. Berlekamp, J. H. Conway, and R. K. Guy, Winning Ways For Your Mathematical Plays, Vol. 1, CRC Press, 2001.
LINKS
M. Lind, E. Fiorini, A. Woldar, and W. H. T. Wong, On Properties of Pebble Assignment Graphs, Journal of Integer Sequences, 24(6), 2020.
EXAMPLE
For n = 4, the a(4) = 5 permutations on [4] with strong fixed points but no small descents: {(1*, 2*, 3*, 4*), (1*, 3, 4, 2), (1*, 4, 2, 3), (2, 3, 1, 4*), (3, 1, 2, 4*)} where * marks strong fixed points.
PROG
(Python) See A346204.
CROSSREFS
KEYWORD
nonn
AUTHOR
Eugene Fiorini, Jared Glassband, Garrison Lee Koch, Sophia Lebiere, Xufei Liu, Evan Sabini, Nathan B. Shank, Andrew Woldar, Jul 09 2021
STATUS
approved