A096577 Number of fixed points of solid partitions under 'time-lapse' operation.

1, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 0, 2, 0, 4

Offset

1,9

Comments

Operation 'time lapse', or 'lapse', L, operates on a solid partition by creating a new one, layer by layer. Layer k is defined by its 3-dimensional-Ferrers plot, equal to the (existence of) elements of the solid partition with value >= k. As if taking a time-lapse picture of the solid partition, filtering out elements less than k and projecting the resulting structure (filled with ones) to the base plane. Given there are three plane to project into, together with the starting solid partition, that makes four 'isomers'.

Links

Table of n, a(n) for n=1..15.

Wouter Meeussen, Solid Partitions Mathematica functions

Example

Solid partition [{{3,1,1,1},{3}},{{2,1}},{{1}},{{1}},{{1}}] lapses (L) into
[{{4,1},{2},{1},{1},{1}},{{1,1},{1}},{{1,1}}], then into
[{{2,1,1,1,1},{2,1},{2}},{{1,1}},{{1}},{{1}}], further into
[{{5,2,1},{2},{1},{1}},{{1,1,1}}] and returns after L^4 to
[{{3,1,1,1},{3}},{{2,1}},{{1}},{{1}},{{1}}]

Mathematica

See link above.

Crossrefs

Cf. A000293, A094504, A094508, A096272, A096573, A096574, A096575, A096576, A096578, A096579, A096580, A096581.

Sequence in context: A008614 A036663 A209457 * A200213 A317839 A137899

Adjacent sequences: A096574 A096575 A096576 * A096578 A096579 A096580

Keyword

more,nonn

Author

Wouter Meeussen, Jun 27 2004

Status

approved