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let p(n) be the number of partition types of an n element set. Find p(1), p(2), p(3), p(4) WHAT IS P[N] ..NOT GIVEN ....OK...TAKING THE N ELEMENT SET AS S=[1,2,3,.....N] ...THEN TAKING NUMBER OF PARTITIONS...P[N] ...LET ME CALL IT INSHORT P ... ..IT MEANS WE HAVE P SUBSETS OF S , SAY S1 , S2 , S3 , .....SP EACH PAIR OF WHICH ARE DISJOINT AND UNION OF ALL EQUALS S.... SO IF WE TAKE A ONE ELEMENT SET S = [1] .....ITS PARTITIONS ARE ONLY 1........P[1]=1...................... TWO ELEMENT SET S = [1,2] .....ITS PARTITIONS ARE [(1),(2)]........P[2]=2............... THREE ELEMENT SET S = [1,2,3] .....ITS PARTITIONS ARE [(1),(2),(3)] ..OR..[(1),(2,3)]..OR..[(2),(1,3)]...OR...[(3),(1,2)]........P[3]=4............... FOUR ELEMENT SET S = [1,2,3,4] .....ITS PARTITIONS ARE....[(1),(2,3,4)]..OR.............[(2),(1,3,4)]...OR...[(3),(1,2,4)]...OR.....[(4),(1,2,3].OR...[(1,2),(3 ,4)]...OR....[(1,3),(2,4)] .....OR.....[(1,4),(2,3)].....P[4]=7...ETC... Solution let p(n) be the number of partition types of an n element set. Find p(1), p(2), p(3), p(4) WHAT IS P[N] ..NOT GIVEN ....OK...TAKING THE N ELEMENT SET AS S=[1,2,3,.....N] ...THEN TAKING NUMBER OF PARTITIONS...P[N] ...LET ME CALL IT INSHORT P ... ..IT MEANS WE HAVE P SUBSETS OF S , SAY S1 , S2 , S3 , .....SP EACH PAIR OF WHICH ARE DISJOINT AND UNION OF ALL EQUALS S.... SO IF WE TAKE A ONE ELEMENT SET S = [1] .....ITS PARTITIONS ARE ONLY 1........P[1]=1...................... TWO ELEMENT SET S = [1,2] .....ITS PARTITIONS ARE [(1),(2)]........P[2]=2............... THREE ELEMENT SET S = [1,2,3] .....ITS PARTITIONS ARE [(1),(2),(3)] ..OR..[(1),(2,3)]..OR..[(2),(1,3)]...OR...[(3),(1,2)]........P[3]=4............... FOUR ELEMENT SET S = [1,2,3,4] .....ITS PARTITIONS ARE....[(1),(2,3,4)]..OR.............[(2),(1,3,4)]...OR...[(3),(1,2,4)]...OR.....[(4),(1,2,3].OR...[(1,2),(3 ,4)]...OR....[(1,3),(2,4)] .....OR.....[(1,4),(2,3)].....P[4]=7...ETC....

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let p(n) be the number of partition types of an n element set. Find p(1), p(2), p(3), p(4) WHAT IS P[N] ..NOT GIVEN ....OK...TAKING THE N ELEMENT SET AS S=[1,2,3,.....N] ...THEN TAKING NUMBER OF PARTITIONS...P[N] ...LET ME CALL IT INSHORT P ... ..IT MEANS WE HAVE P SUBSETS OF S , SAY S1 , S2 , S3 , .....SP EACH PAIR OF WHICH ARE DISJOINT AND UNION OF ALL EQUALS S.... SO IF WE TAKE A ONE ELEMENT SET S = [1] .....ITS PARTITIONS ARE ONLY 1........P[1]=1...................... TWO ELEMENT SET S = [1,2] .....ITS PARTITIONS ARE [(1),(2)]........P[2]=2............... THREE ELEMENT SET S = [1,2,3] .....ITS PARTITIONS ARE [(1),(2),(3)] ..OR..[(1),(2,3)]..OR..[(2),(1,3)]...OR...[(3),(1,2)]........P[3]=4............... FOUR ELEMENT SET S = [1,2,3,4] .....ITS PARTITIONS ARE....[(1),(2,3,4)]..OR.............[(2),(1,3,4)]...OR...[(3),(1,2,4)]...OR.....[(4),(1,2,3].OR...[(1,2),(3 ,4)]...OR....[(1,3),(2,4)] .....OR.....[(1,4),(2,3)].....P[4]=7...ETC... Solution let p(n) be the number of partition types of an n element set. Find p(1), p(2), p(3), p(4) WHAT IS P[N] ..NOT GIVEN ....OK...TAKING THE N ELEMENT SET AS S=[1,2,3,.....N] ...THEN TAKING NUMBER OF PARTITIONS...P[N] ...LET ME CALL IT INSHORT P ... ..IT MEANS WE HAVE P SUBSETS OF S , SAY S1 , S2 , S3 , .....SP EACH PAIR OF WHICH ARE DISJOINT AND UNION OF ALL EQUALS S.... SO IF WE TAKE A ONE ELEMENT SET S = [1] .....ITS PARTITIONS ARE ONLY 1........P[1]=1...................... TWO ELEMENT SET S = [1,2] .....ITS PARTITIONS ARE [(1),(2)]........P[2]=2............... THREE ELEMENT SET S = [1,2,3] .....ITS PARTITIONS ARE [(1),(2),(3)] ..OR..[(1),(2,3)]..OR..[(2),(1,3)]...OR...[(3),(1,2)]........P[3]=4............... FOUR ELEMENT SET S = [1,2,3,4] .....ITS PARTITIONS ARE....[(1),(2,3,4)]..OR.............[(2),(1,3,4)]...OR...[(3),(1,2,4)]...OR.....[(4),(1,2,3].OR...[(1,2),(3 ,4)]...OR....[(1,3),(2,4)] .....OR.....[(1,4),(2,3)].....P[4]=7...ETC...

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let p(n) be the number of partition types of an n element set. Find.pdf

  • 1. let p(n) be the number of partition types of an n element set. Find p(1), p(2), p(3), p(4) WHAT IS P[N] ..NOT GIVEN ....OK...TAKING THE N ELEMENT SET AS S=[1,2,3,.....N] ...THEN TAKING NUMBER OF PARTITIONS...P[N] ...LET ME CALL IT INSHORT P ... ..IT MEANS WE HAVE P SUBSETS OF S , SAY S1 , S2 , S3 , .....SP EACH PAIR OF WHICH ARE DISJOINT AND UNION OF ALL EQUALS S.... SO IF WE TAKE A ONE ELEMENT SET S = [1] .....ITS PARTITIONS ARE ONLY 1........P[1]=1...................... TWO ELEMENT SET S = [1,2] .....ITS PARTITIONS ARE [(1),(2)]........P[2]=2............... THREE ELEMENT SET S = [1,2,3] .....ITS PARTITIONS ARE [(1),(2),(3)] ..OR..[(1),(2,3)]..OR..[(2),(1,3)]...OR...[(3),(1,2)]........P[3]=4............... FOUR ELEMENT SET S = [1,2,3,4] .....ITS PARTITIONS ARE....[(1),(2,3,4)]..OR.............[(2),(1,3,4)]...OR...[(3),(1,2,4)]...OR.....[(4),(1,2,3].OR...[(1,2),(3 ,4)]...OR....[(1,3),(2,4)] .....OR.....[(1,4),(2,3)].....P[4]=7...ETC... Solution let p(n) be the number of partition types of an n element set. Find p(1), p(2), p(3), p(4) WHAT IS P[N] ..NOT GIVEN ....OK...TAKING THE N ELEMENT SET AS S=[1,2,3,.....N] ...THEN TAKING NUMBER OF PARTITIONS...P[N] ...LET ME CALL IT INSHORT P ... ..IT MEANS WE HAVE P SUBSETS OF S , SAY S1 , S2 , S3 , .....SP EACH PAIR OF WHICH ARE DISJOINT AND UNION OF ALL EQUALS S.... SO IF WE TAKE A ONE ELEMENT SET S = [1] .....ITS PARTITIONS ARE ONLY 1........P[1]=1...................... TWO ELEMENT SET S = [1,2] .....ITS PARTITIONS ARE [(1),(2)]........P[2]=2............... THREE ELEMENT SET S = [1,2,3] .....ITS PARTITIONS ARE [(1),(2),(3)] ..OR..[(1),(2,3)]..OR..[(2),(1,3)]...OR...[(3),(1,2)]........P[3]=4............... FOUR ELEMENT SET S = [1,2,3,4] .....ITS PARTITIONS ARE....[(1),(2,3,4)]..OR.............[(2),(1,3,4)]...OR...[(3),(1,2,4)]...OR.....[(4),(1,2,3].OR...[(1,2),(3 ,4)]...OR....[(1,3),(2,4)] .....OR.....[(1,4),(2,3)].....P[4]=7...ETC...