The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A114736

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A114736

Number of planar partitions of n where parts strictly decrease along each row and column.
(history; published version)

#23 by Andrey Zabolotskiy at Wed Jan 12 09:50:25 EST 2022

STATUS

editing

approved

#22 by Andrey Zabolotskiy at Wed Jan 12 09:50:21 EST 2022

MATHEMATICA

prs2mat[prs_]:=Table[Count[prs, {i, j}], {i, Union[First/@prs]}, {j, Union[Last/@prs]}];

multsubs[set_, k_]:=If[k==0, {{}}, Join@@Table[Prepend[#, set[[i]]]&/@multsubs[Drop[set, i-1], k-1], {i, Length[set]}]];

Table[Length[Select[multsubs[Tuples[Range[n], 2], n], And[Union[First/@#]==Range[Max@@First/@#], Union[Last/@#]==Range[Max@@Last/@#], And@@(OrderedQ[#, Greater]&/@prs2mat[#]), And@@(OrderedQ[#, Greater]&/@Transpose[prs2mat[#]])]&]], {n, 5}] (* Gus Wiseman, Nov 15 2018 *)

PROG

prs2mat[prs_]:=Table[Count[prs, {i, j}], {i, Union[First/@prs]}, {j, Union[Last/@prs]}];

multsubs[set_, k_]:=If[k==0, {{}}, Join@@Table[Prepend[#, set[[i]]]&/@multsubs[Drop[set, i-1], k-1], {i, Length[set]}]];

STATUS

approved

editing

#21 by Susanna Cuyler at Fri Nov 16 07:48:41 EST 2018

STATUS

proposed

approved

#20 by Gus Wiseman at Thu Nov 15 22:15:21 EST 2018

STATUS

editing

proposed

#19 by Gus Wiseman at Thu Nov 15 22:14:05 EST 2018

CROSSREFS

Cf. A000009, A000219, A001970, A007716, A068313, A117433, A000009A120733, A319646, A321645, A321652, A321653, A321655.

Cf. A001970, A007716, A068313, A114736, A120733, A319646, A321645, A321652, A321653, A321655.

#18 by Gus Wiseman at Thu Nov 15 21:40:22 EST 2018

EXAMPLE

From Gus Wiseman, Nov 15 2018: (Start)

The a(6) = 10 plane partitions:

6 5 1 4 2 3 2 1

.

5 4 1 4 3 2 3 1

1 1 2 1 2

.

3

2

1

(End)

PROG

prs2mat[prs_]:=Table[Count[prs, {i, j}], {i, Union[First/@prs]}, {j, Union[Last/@prs]}];

multsubs[set_, k_]:=If[k==0, {{}}, Join@@Table[Prepend[#, set[[i]]]&/@multsubs[Drop[set, i-1], k-1], {i, Length[set]}]];

CROSSREFS

Cf. A001970, A007716, A068313, A114736, A120733, A319646, A321645, A321652, A321653, A321655.

STATUS

approved

editing

#17 by Alois P. Heinz at Wed Sep 26 19:12:25 EDT 2018

STATUS

editing

approved

#16 by Alois P. Heinz at Wed Sep 26 19:12:22 EDT 2018

LINKS

Alois P. Heinz, <a href="/A114736/b114736.txt">Table of n, a(n) for n = 0..85</a>

#15 by Alois P. Heinz at Wed Sep 26 18:12:02 EDT 2018

KEYWORD

more,nonn,changed

EXTENSIONS

a(40)-a(44) from Alois P. Heinz, Sep 26 2018

#14 by Alois P. Heinz at Wed Sep 26 18:11:18 EDT 2018

DATA

1, 1, 1, 3, 4, 6, 10, 15, 22, 33, 49, 70, 102, 146, 205, 290, 405, 561, 779, 1071, 1463, 1999, 2714, 3667, 4946, 6641, 8880, 11848, 15753, 20870, 27586, 36354, 47766, 62621, 81878, 106785, 138975, 180449, 233778, 302270, 390027, 502256, 645603, 828330, 1060851

STATUS

approved

editing