Integer partitions - 편집 역사

2020년 12월 28일 (월) 12:18에 Pythagoras0님의 편집

2020-12-28T12:18:32Z

2020년 11월 16일 (월) 15:52에 Pythagoras0님의 편집

2020-11-16T15:52:11Z

2020년 11월 16일 (월) 14:47에 Pythagoras0님의 편집

2020-11-16T14:47:10Z

2020년 11월 13일 (금) 15:22에 imported>Pythagoras0님의 편집

2020-11-13T15:22:02Z

2012년 10월 29일 (월) 17:55에 imported>Pythagoras0님의 편집

2012-10-29T17:55:16Z

2012년 10월 29일 (월) 17:53에 imported>Pythagoras0님의 편집

2012-10-29T17:53:16Z

imported>Pythagoras0: 찾아 바꾸기 – “

” 문자열을 “==” 문자열로

2012-10-28T22:29:39Z

찾아 바꾸기 – “</h5>” 문자열을 “==” 문자열로

imported>Pythagoras0: 찾아 바꾸기 – “

” 문자열을 “==” 문자열로

2012-10-28T21:07:24Z

찾아 바꾸기 – “<h5>” 문자열을 “==” 문자열로

2011년 4월 23일 (토) 22:05에 http://bomber0.myid.net/님의 편집

2011-04-23T22:05:02Z

http://bomber0.myid.net/: 피타고라스님이 이 페이지의 위치를 q-series페이지로 이동하였습니다.

2010-03-20T02:33:10Z

피타고라스님이 이 페이지의 위치를 <a href="/pages/4727637">q-series</a>페이지로 이동하였습니다.

@@ 5번째 줄: / 5번째 줄: @@
 md:=5
-−
 n:=12
@@ 11번째 줄: / 11번째 줄: @@
 md:=7
-−
-−
 n:=6
@@ 19번째 줄: / 19번째 줄: @@
 md:=11
-−
-−
 will be a good choice
-−
 <math>p(5k+4)\equiv 0 \pmod 5</math>
@@ 33번째 줄: / 33번째 줄: @@
 <math>p(11k+6)\equiv 0 \pmod {11}</math>
-−
-−
 ==partition rank and crank==
-(*define a integer you want to investigate*)n := 6 (*choose the proper moduli for the partition statistics*) md := 2 S[n_] := IntegerPartitions[n] (*define the rank of a partition with the name "pr"*) pr[s_] := Max[s] - Length[s] (*define the crank of a partition with the name "crank"*) Om[s_] := Count[s, 1] Mu[s_] := Length[Select[s, # > Om[s] &]] crank[s_] := If[Om[s] == 0, Max[s], Mu[s] - Om[s]] (*modulus distribution of partition rank*) Sort[Tally[Table[Mod[pr[s], md], {s, S[n]}]]] (*modulus distribution of partition crank*) Sort[Tally[Table[Mod[crank[s], md], {s, S[n]}]]] (*list of paritions with rank& crank*) Do[Print[s, ", rank=", pr[s], "\[Congruent]", Mod[pr[s], md], "(mod ",    md, ")", ", crank=", crank[s], "\[Congruent]", Mod[crank[s], md],   "(mod ", md, ")"], {s, S[n]}] (*you will see the distribution of rank/crank modulus,the partition \ statistics and list of paritions with rank&crank*)
+(*define a integer you want to investigate*)n := 6 (*choose the proper moduli for the partition statistics*) md := 2 S[n_] := IntegerPartitions[n] (*define the rank of a partition with the name "pr"*) pr[s_] := Max[s] - Length[s] (*define the crank of a partition with the name "crank"*) Om[s_] := Count[s, 1] Mu[s_] := Length[Select[s, # > Om[s] &]] crank[s_] := If[Om[s] == 0, Max[s], Mu[s] - Om[s]] (*modulus distribution of partition rank*) Sort[Tally[Table[Mod[pr[s], md], {s, S[n]}]]] (*modulus distribution of partition crank*) Sort[Tally[Table[Mod[crank[s], md], {s, S[n]}]]] (*list of paritions with rank& crank*) Do[Print[s, ", rank=", pr[s], "\[Congruent]", Mod[pr[s], md], "(mod ",    md, ")", ", crank=", crank[s], "\[Congruent]", Mod[crank[s], md],   "(mod ", md, ")"], {s, S[n]}] (*you will see the distribution of rank/crank modulus,the partition \ statistics and list of paritions with rank&crank*)
-−
-−
 ==number of partitions with odd and even rank==
@@ 51번째 줄: / 51번째 줄: @@
 S[n_] := IntegerPartitions[n] pr[s_] := Max[s] - Length[s] PrOd[n_] := Length[Select[S[n], OddQ[pr[#]] &]] PrEv[n_] := Length[Select[S[n], EvenQ[pr[#]] &]] alpha[n_] := PrEv[n] - PrOd[n] Table[alpha[n], {n, 1, 20}]
-−
-−
 *  the generating function is can be shown by Series[(1 + 4 Sum[(-1)^n q^(n (3 n + 1)/2)/(1 + q^n), {n, 1, 10}])/Sum[(-1)^n q^(n (3 n + 1)/2), {n, -8, 8}], {q, 0, 100}]
-−
 ==various partitions==
@@ 65번째 줄: / 65번째 줄: @@
   (* partition into exactly three parts *) VS[n_] := IntegerPartitions[n, {3}] VS[11]
-−
   (* number of partitions into distinct parts *) PartitionsQ[11]
-−
 (* partition into odd parts *) IntegerPartitions[11, All, {1, 3, 5, 7, 9, 11}]
 [[분류:math and physics]]
 [[분류:migrate]]

@@ 72번째 줄: / 72번째 줄: @@
 (* partition into odd parts *) IntegerPartitions[11, All, {1, 3, 5, 7, 9, 11}]
 [[분류:math and physics]]
 [[분류:migrate]]

@@ 39번째 줄: / 39번째 줄: @@
 ==partition rank and crank==
-(*define a integer you want to investigate*)n := 6<br> (*choose the proper moduli for the partition statistics*)<br> md := 2<br> S[n_] := IntegerPartitions[n]<br> (*define the rank of a partition with the name "pr"*)<br> pr[s_] := Max[s] - Length[s]<br> (*define the crank of a partition with the name "crank"*)<br> Om[s_] := Count[s, 1]<br> Mu[s_] := Length[Select[s, # > Om[s] &]]<br> crank[s_] := If[Om[s] == 0, Max[s], Mu[s] - Om[s]]<br> (*modulus distribution of partition rank*)<br> Sort[Tally[Table[Mod[pr[s], md], {s, S[n]}]]]<br> (*modulus distribution of partition crank*)<br> Sort[Tally[Table[Mod[crank[s], md], {s, S[n]}]]]<br> (*list of paritions with rank& crank*)<br> Do[Print[s, ", rank=", pr[s], "\[Congruent]", Mod[pr[s], md], "(mod ",<br>    md, ")", ", crank=", crank[s], "\[Congruent]", Mod[crank[s], md],<br>   "(mod ", md, ")"], {s, S[n]}]<br> (*you will see the distribution of rank/crank modulus,the partition \<br> statistics and list of paritions with rank&crank*)
+(*define a integer you want to investigate*)n := 6 (*choose the proper moduli for the partition statistics*) md := 2 S[n_] := IntegerPartitions[n] (*define the rank of a partition with the name "pr"*) pr[s_] := Max[s] - Length[s] (*define the crank of a partition with the name "crank"*) Om[s_] := Count[s, 1] Mu[s_] := Length[Select[s, # > Om[s] &]] crank[s_] := If[Om[s] == 0, Max[s], Mu[s] - Om[s]] (*modulus distribution of partition rank*) Sort[Tally[Table[Mod[pr[s], md], {s, S[n]}]]] (*modulus distribution of partition crank*) Sort[Tally[Table[Mod[crank[s], md], {s, S[n]}]]] (*list of paritions with rank& crank*) Do[Print[s, ", rank=", pr[s], "\[Congruent]", Mod[pr[s], md], "(mod ",    md, ")", ", crank=", crank[s], "\[Congruent]", Mod[crank[s], md],   "(mod ", md, ")"], {s, S[n]}] (*you will see the distribution of rank/crank modulus,the partition \ statistics and list of paritions with rank&crank*)
@@ 49번째 줄: / 49번째 줄: @@
 * for theoretical background, see [[rank of partition and mock theta conjecture|rank of partition and mock theta function]]
-S[n_] := IntegerPartitions[n]<br> pr[s_] := Max[s] - Length[s]<br> PrOd[n_] := Length[Select[S[n], OddQ[pr[#]] &]]<br> PrEv[n_] := Length[Select[S[n], EvenQ[pr[#]] &]]<br> alpha[n_] := PrEv[n] - PrOd[n]<br> Table[alpha[n], {n, 1, 20}]
+S[n_] := IntegerPartitions[n] pr[s_] := Max[s] - Length[s] PrOd[n_] := Length[Select[S[n], OddQ[pr[#]] &]] PrEv[n_] := Length[Select[S[n], EvenQ[pr[#]] &]] alpha[n_] := PrEv[n] - PrOd[n] Table[alpha[n], {n, 1, 20}]
@@ 55번째 줄: / 55번째 줄: @@
-*  the generating function is can be shown by<br> Series[(1 + 4 Sum[(-1)^n q^(n (3 n + 1)/2)/(1 + q^n), {n, 1, 10}])/Sum[(-1)^n q^(n (3 n + 1)/2), {n, -8, 8}], {q, 0, 100}]<br>
+*  the generating function is can be shown by Series[(1 + 4 Sum[(-1)^n q^(n (3 n + 1)/2)/(1 + q^n), {n, 1, 10}])/Sum[(-1)^n q^(n (3 n + 1)/2), {n, -8, 8}], {q, 0, 100}]
@@ 61번째 줄: / 61번째 줄: @@
 ==various partitions==
-(* partitions with at most 5 parts *)<br> IntegerPartitions[7, 5]
+(* partitions with at most 5 parts *) IntegerPartitions[7, 5]
-<br> (* partition into exactly three parts *)<br> VS[n_] := IntegerPartitions[n, {3}]<br> VS[11]
+ (* partition into exactly three parts *) VS[n_] := IntegerPartitions[n, {3}] VS[11]
-<br> (* number of partitions into distinct parts *)<br> PartitionsQ[11]
+ (* number of partitions into distinct parts *) PartitionsQ[11]
-(* partition into odd parts *)<br> IntegerPartitions[11, All, {1, 3, 5, 7, 9, 11}]
+(* partition into odd parts *) IntegerPartitions[11, All, {1, 3, 5, 7, 9, 11}]
 [[분류:math and physics]]
 [[분류:math and physics]]
 [[분류:migrate]]

← 이전 판		2020년 11월 13일 (금) 15:22 판
74번째 줄:		74번째 줄:
	[[분류:math and physics]]		[[분류:math and physics]]
	[[분류:math and physics]]		[[분류:math and physics]]
		+	[[분류:migrate]]

← 이전 판		2012년 10월 29일 (월) 17:55 판
72번째 줄:		72번째 줄:

	(* partition into odd parts *)<br> IntegerPartitions[11, All, {1, 3, 5, 7, 9, 11}]		(* partition into odd parts *)<br> IntegerPartitions[11, All, {1, 3, 5, 7, 9, 11}]
		+	[[분류:math and physics]]
	[[분류:math and physics]]		[[분류:math and physics]]

← 이전 판		2012년 10월 29일 (월) 17:53 판
72번째 줄:		72번째 줄:

	(* partition into odd parts *)<br> IntegerPartitions[11, All, {1, 3, 5, 7, 9, 11}]		(* partition into odd parts *)<br> IntegerPartitions[11, All, {1, 3, 5, 7, 9, 11}]
		+	[[분류:math and physics]]

@@ 1번째 줄: / 1번째 줄: @@
-==background</h5>
+==background==
 n:=9
@@ 37번째 줄: / 37번째 줄: @@
-==partition rank and crank</h5>
+==partition rank and crank==
 (*define a integer you want to investigate*)n := 6<br> (*choose the proper moduli for the partition statistics*)<br> md := 2<br> S[n_] := IntegerPartitions[n]<br> (*define the rank of a partition with the name "pr"*)<br> pr[s_] := Max[s] - Length[s]<br> (*define the crank of a partition with the name "crank"*)<br> Om[s_] := Count[s, 1]<br> Mu[s_] := Length[Select[s, # > Om[s] &]]<br> crank[s_] := If[Om[s] == 0, Max[s], Mu[s] - Om[s]]<br> (*modulus distribution of partition rank*)<br> Sort[Tally[Table[Mod[pr[s], md], {s, S[n]}]]]<br> (*modulus distribution of partition crank*)<br> Sort[Tally[Table[Mod[crank[s], md], {s, S[n]}]]]<br> (*list of paritions with rank& crank*)<br> Do[Print[s, ", rank=", pr[s], "\[Congruent]", Mod[pr[s], md], "(mod ",<br>    md, ")", ", crank=", crank[s], "\[Congruent]", Mod[crank[s], md],<br>   "(mod ", md, ")"], {s, S[n]}]<br> (*you will see the distribution of rank/crank modulus,the partition \<br> statistics and list of paritions with rank&crank*)
@@ 45번째 줄: / 45번째 줄: @@
-==number of partitions with odd and even rank</h5>
+==number of partitions with odd and even rank==
 * for theoretical background, see [[rank of partition and mock theta conjecture|rank of partition and mock theta function]]
@@ 59번째 줄: / 59번째 줄: @@
-==various partitions</h5>
+==various partitions==
 (* partitions with at most 5 parts *)<br> IntegerPartitions[7, 5]

← 이전 판		2011년 4월 23일 (토) 22:05 판
55번째 줄:		55번째 줄:


−	* the ~~generatinf~~ function is can be shown by<br> Series[(1 + 4 Sum[(-1)^n q^(n (3 n + 1)/2)/(1 + q^n), {n, 1, 10}])/Sum[(-1)^n q^(n (3 n + 1)/2), {n, -8, 8}], {q, 0, 100}]<br>	+	* the generating function is can be shown by<br> Series[(1 + 4 Sum[(-1)^n q^(n (3 n + 1)/2)/(1 + q^n), {n, 1, 10}])/Sum[(-1)^n q^(n (3 n + 1)/2), {n, -8, 8}], {q, 0, 100}]<br>

← 이전 판	2010년 3월 20일 (토) 02:33 판
(차이 없음)