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A324324
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MM-numbers of crossing set partitions.
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6
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2117, 3973, 4843, 5891, 6757, 7181, 7801, 10019, 10063, 11051, 11567, 13021, 13193, 13459, 14123, 14921, 17603, 18407, 18761, 18877, 19307, 19633, 20941, 21083, 21251, 21457, 22849, 23519, 23533, 24727, 26101, 27133, 27169, 27173, 27413, 29111, 30479, 31261
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OFFSET
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1,1
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COMMENTS
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A multiset multisystem is a finite multiset of finite multisets. A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. The multiset multisystem with MM-number n is formed by taking the multiset of prime indices of each part in the multiset of prime indices of n. For example, the prime indices of 78 are {1,2,6}, so the multiset multisystem with MM-number 78 is {{},{1},{1,2}}.
A multiset multisystem is crossing if it contains two parts of the form {{...x...y...},{...z...t...}} with x < z < y < t or z < x < t < y.
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LINKS
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MATHEMATICA
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croXQ[stn_]:=MatchQ[stn, {___, {___, x_, ___, y_, ___}, ___, {___, z_, ___, t_, ___}, ___}/; x<z<y<t||z<x<t<y];
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
setptnQ[bks_]:=UnsameQ@@Join@@bks&&!MemberQ[bks, {}];
Select[Range[10000], And[croXQ[primeMS/@primeMS[#]], setptnQ[primeMS/@primeMS[#]]]&]
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CROSSREFS
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Cf. A000108 (non-crossing set partitions), A001055, A001222, A003963, A005117, A016098 (crossing set partitions), A054726, A056239, A112798, A302242, A302243, A302505, A302521 (MM-numbers of set partitions).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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