login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A317076 Number of connected antichains of multisets with multiset-join a strongly normal multiset of size n. 5
1, 1, 2, 8, 110, 7047 (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) = 8 connected antichains of multisets:

(111),

(112), (11)(12),

(123), (13)(23), (12)(23), (12)(13), (12)(13)(23).

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}]]];

csm[s_]:=With[{c=Select[Tuples[Range[Length[s]], 2], And[OrderedQ[#], UnsameQ@@#, Length[Intersection@@s[[#]]]>0]&]}, If[c=={}, s, csm[Union[Append[Delete[s, List/@c[[1]]], multijoin@@s[[c[[1]]]]]]]]];

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

cuu[m_]:=Select[stableSets[Union[Rest[Subsets[m]]], submultisetQ], And[multijoin@@#==m, Length[csm[#]]==1]&];

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

CROSSREFS

Cf. A048143, A255906, A286520, A303837, A303838, A304716, A305001, A305078.

Cf. A317074, A317075, A317078, A317080.

Sequence in context: A132523 A012554 A012665 * A211938 A331405 A005787

Adjacent sequences: A317073 A317074 A317075 * A317077 A317078 A317079

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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 2 05:20 EST 2022. Contains 358485 sequences. (Running on oeis4.)