OFFSET
1,2
COMMENTS
REFERENCES
E. Lundberg and B. Nagle, A permutation statistic arising in dynamics of internal maps. (submitted, 2013)
LINKS
E. Clark and R. Ehrenborg, Explicit expressions for the extremal excedance statistic, European J. Combinatorics, 31, 2010, 270-279.
J. Cooper, E. Lundberg, and B. Nagle, Generalized pattern frequency in large permutations, Electron. J. Combin. 20, 2013, #P28.
FORMULA
The values of T(n,k) have been found by straightforward counting (with Maple). The Maple program yields the generating polynomial of the specified row n. Within the program, sp(p) is the number of stretching pairs of the permutation p.
EXAMPLE
T(4,1) = 2 because 2143 has 1 stretching pair (2,3) and 3142 has 1 stretching pair (2,3); the other 22 permutations in S_4 have no stretching pairs.
Triangle starts:
1;
2;
6;
22, 2;
94, 22, 4;
462, 172, 72, 12, 2;
2582, 1244, 824, 276, 94, 16, 4;
MAPLE
n := 7: with(combinat): sp := proc (p) local ct, i, j: ct := 0: for i from 2 to nops(p)-2 do for j from i+1 to nops(p)-1 do if p[i] < i and i < j and j < p[j] then ct := ct+1 else end if end do end do: ct end proc: P := permute(n): f[n] := sort(add(t^sp(P[j]), j = 1 .. factorial(n)));
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Emeric Deutsch, Feb 26 2013
STATUS
approved