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A116540 Number of zero-one matrices with n ones and no zero rows or columns, up to permutation of rows. 13
1, 3, 10, 41, 192, 1025, 6087, 39754, 282241, 2159916, 17691161, 154192692, 1423127819, 13851559475, 141670442163, 1517880400352, 16989834719706, 198191448685735, 2404300796114642, 30273340418567819, 394948562421362392 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also number of normal set multipartitions of weight n. These are defined as multisets of sets that together partition a normal multiset of weight n, where a multiset is normal if it spans an initial interval of positive integers. Set multipartitions are involved in the expansion of elementary symmetric functions in terms of augmented monomial symmetric functions. - Gus Wiseman, Oct 22 2015

LINKS

Table of n, a(n) for n=1..21.

P. J. Cameron, T. Prellberg and D. Stark, Asymptotics for incidence matrix classes , arXiv:math/0510155 [math.CO], 2005-2006.

M. Klazar, Extremal problems for ordered hypergraphs, arXiv:math/0305048 [math.CO], 2003.

Gus Wiseman, Four symmetric function identities

EXAMPLE

The a(3) = 10 normal set multipartitions are: {1,1,1}, {1,12}, {1,1,2}, {2,12}, {1,2,2}, {123}, {1,23}, {2,13}, {3,12}, {1,2,3}.

MATHEMATICA

MSOSA[s_List] :=

  MSOSA[s] = If[Length[s] === 0, {{}}, Module[{sbs, fms},

     sbs = Rest[Subsets[Union[s]]];

     fms =

      Function[r,

        Append[#, r] & /@

         MSOSA[Fold[DeleteCases[#1, #2, {1}, 1] &, s, r]]] /@ sbs;

     Select[Join @@ fms, OrderedQ]

     ]];

mmallnorm[n_Integer] :=

  Function[s, Array[Count[s, y_ /; y <= #] + 1 &, n]] /@

   Subsets[Range[n - 1] + 1];

Array[Plus @@ Length /@ MSOSA /@ mmallnorm[#] &, 9]

(* Gus Wiseman, Oct 22 2015 *)

CROSSREFS

Cf. A049311, A101370.

Sequence in context: A151083 A140046 A260772 * A236407 A000248 A245504

Adjacent sequences:  A116537 A116538 A116539 * A116541 A116542 A116543

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Mar 27 2006

STATUS

approved

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Last modified June 23 09:44 EDT 2018. Contains 305694 sequences. (Running on oeis4.)