login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A317074 Number of antichains of multisets with multiset-join a strongly normal multiset of size n. 5
1, 1, 3, 13, 148, 7685 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

An antichain of multisets is a finite set of finite nonempty multisets, none of which is a submultiset of any other. A multiset is strongly normal if it spans an initial interval of positive integers with weakly decreasing multiplicities. The multiset-join of a multiset system has the same vertices with multiplicities equal to the maxima of the multiplicities in the edges.

LINKS

Table of n, a(n) for n=0..5.

Goran Kilibarda and Vladeta Jovovic, Antichains of Multisets, Journal of Integer Sequences, Vol. 7 (2004).

EXAMPLE

The a(3) = 13 antichains of multisets:

  (111),

  (112), (11)(12), (2)(11),

  (123), (13)(23), (12)(23), (12)(13), (12)(13)(23), (3)(12), (2)(13), (1)(23), (1)(2)(3).

MATHEMATICA

stableSets[u_, Q_]:=If[Length[u]==0, {{}}, With[{w=First[u]}, Join[stableSets[DeleteCases[u, w], Q], Prepend[#, w]&/@stableSets[DeleteCases[u, r_/; r==w||Q[r, w]||Q[w, r]], Q]]]];

multijoin[mss__]:=Join@@Table[Table[x, {Max[Count[#, x]&/@{mss}]}], {x, Union[mss]}];

submultisetQ[M_, N_]:=Or[Length[M]==0, MatchQ[{Sort[List@@M], Sort[List@@N]}, {{x_, Z___}, {___, x_, W___}}/; submultisetQ[{Z}, {W}]]];

strnorm[n_]:=Flatten[MapIndexed[Table[#2, {#1}]&, #]]&/@IntegerPartitions[n];

auu[m_]:=Select[stableSets[Union[Rest[Subsets[m]]], submultisetQ], multijoin@@#==m&];

Table[Length[Join@@Table[auu[m], {m, strnorm[n]}]], {n, 5}]

CROSSREFS

Cf. A048143, A285572, A293993, A293994, A303837, A303838, A304998, A305001.

Cf. A317073, A317076, A317078, A317079.

Sequence in context: A001150 A108554 A287029 * A230036 A014376 A224990

Adjacent sequences:  A317071 A317072 A317073 * A317075 A317076 A317077

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Jul 20 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 21 04:22 EST 2019. Contains 329350 sequences. (Running on oeis4.)