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| − | <h5> | + | <h5>partition and rank</h5> |
<< Combinatorica`<br> (*define a integer you want to investigate*)<br> n := 12<br> (* choose the proper moduli for the partition statistics *)<br> md := 7<br> S[n_] := Partitions[n]<br> (*define the rank of a partition with the name "pr"*)<br> pr[s_] := Max[s] - Length[s]<br> S[n]<br> PartitionsP[n]<br> (*partition statistics*)<br> Table[Mod[pr[s], md], {s, S[n]}]<br> Sort[%]<br> (*list of paritions with rank*)<br> Do[Print[s, ", rank=", pr[s], "\[Congruent]",<br> Mod[Max[s] - Length[s], md], "(mod ", md, ")"], {s, S[n]}]<br> (*you will see p (n), the partition statistics and list of paritions \<br> with rank*) | << Combinatorica`<br> (*define a integer you want to investigate*)<br> n := 12<br> (* choose the proper moduli for the partition statistics *)<br> md := 7<br> S[n_] := Partitions[n]<br> (*define the rank of a partition with the name "pr"*)<br> pr[s_] := Max[s] - Length[s]<br> S[n]<br> PartitionsP[n]<br> (*partition statistics*)<br> Table[Mod[pr[s], md], {s, S[n]}]<br> Sort[%]<br> (*list of paritions with rank*)<br> Do[Print[s, ", rank=", pr[s], "\[Congruent]",<br> Mod[Max[s] - Length[s], md], "(mod ", md, ")"], {s, S[n]}]<br> (*you will see p (n), the partition statistics and list of paritions \<br> with rank*) | ||
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| + | <h5>pa</h5> | ||
2010년 3월 4일 (목) 21:28 판
background
n:=9
md:=5
n:=12
md:=7
will be a good choice
partition and rank
<< Combinatorica`
(*define a integer you want to investigate*)
n := 12
(* choose the proper moduli for the partition statistics *)
md := 7
S[n_] := Partitions[n]
(*define the rank of a partition with the name "pr"*)
pr[s_] := Max[s] - Length[s]
S[n]
PartitionsP[n]
(*partition statistics*)
Table[Mod[pr[s], md], {s, S[n]}]
Sort[%]
(*list of paritions with rank*)
Do[Print[s, ", rank=", pr[s], "\[Congruent]",
Mod[Max[s] - Length[s], md], "(mod ", md, ")"], {s, S[n]}]
(*you will see p (n), the partition statistics and list of paritions \
with rank*)