OFFSET
1,2
COMMENTS
This is the sum over the matrix of base change from the elementary symmetric functions to the monomial symmetric functions.
REFERENCES
I. G. Macdonald, Symmetric Functions and Hall Polynomials, Oxford 1979, p. 57.
LINKS
Ludovic Schwob, Table of n, a(n) for n = 1..37
EXAMPLE
a(2) = 4 because there are 4 different 0-1 matrices of weight 2: 1 10 01 11,1, 01, 10.
From Gus Wiseman, Nov 15 2018: (Start)
The a(3) = 15 matrices:
[1 1 1]
.
[1 1] [1 1 0] [1 0 1] [0 1 1]
[1 0] [0 0 1] [0 1 0] [1 0 0]
.
[1] [1 0] [1 0] [1 0 0] [1 0 0] [0 1] [0 1 0] [0 1 0] [0 0 1] [0 0 1]
[1] [1 0] [0 1] [0 1 0] [0 0 1] [1 0] [1 0 0] [0 0 1] [1 0 0] [0 1 0]
[1] [0 1] [1 0] [0 0 1] [0 1 0] [1 0] [0 0 1] [1 0 0] [0 1 0] [1 0 0]
(End)
MATHEMATICA
prs2mat[prs_]:=Table[Count[prs, {i, j}], {i, Union[First/@prs]}, {j, Union[Last/@prs]}];
Table[Length[Select[Subsets[Tuples[Range[n], 2], {n}], And[Union[First/@#]==Range[Max@@First/@#], Union[Last/@#]==Range[Max@@Last/@#], OrderedQ[Total/@prs2mat[#]], OrderedQ[Total/@T[prs2mat[#]]]]&]], {n, 5}] (* Gus Wiseman, Nov 15 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Axel Kohnert (axel.kohnert(AT)uni-bayreuth.de), Feb 25 2002
EXTENSIONS
Name changed by Gus Wiseman, Nov 15 2018
a(20) onwards from Ludovic Schwob, Oct 13 2023
STATUS
approved