■幾何分布と誕生日の問題(その21)

Q(x)・R(x)=x(x+1)(x^2+1)(x^2+x+1)(x^2−x+1)(x^4−x^2+1)

の続きである.

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[1]

  Q(x)=x(x+1)(x^2+1)(x^2+x+1)=x+2x^2+3x^3+3x^4+2x^5+x^6→12面体サイコロ{1,2,2,3,3,3,4,4,4,5,5,6}

  R(x)=(x^2−x+1)(x^4−x^2+1)=1−x+x^3−x^5+x^6→不適

[2]

  Q(x)=x(x+1)(x^2+1)(x^2−x+1)=x+x^2+x^7+x^8→4面体サイコロ{1,2,7,8}

  R(x)=(x^2+x+1)(x^4−x^2+1)=1+x−x^3+x^5+x^6→不適

[3]

  Q(x)=x(x+1)(x^2+1)(x^4−x^2+1)=x+x^2+x^7+x^8→4面体サイコロ{1,2,7,8}

  R(x)=(x^2+x+1)(x^2−x+1)=1+x^2+x^4→3面体サイコロ{0,2,4}

[4]

  Q(x)=x(x+1)(x^2+x+1)(x^2−x+1)=x+x^2+x^3+x^4+x^5+x^6→6面体サイコロ{1,2,3,4,5,6}

  R(x)=(x^2+1)(x^4−x^2+1)=1+x^6→2面体サイコロ{0,6}

[5]

  Q(x)=x(x+1)(x^2+x+1)(x^4−x^2+1)

=x+2x^2+x^3−x4+x^5+x^6+2x^7+x^8→不適

[6]

  Q(x)=x(x+1)(x^2−x+1)(x^4−x^2+1)

=(x^4+x)(x^4−x^2+1)=x−x^3+x^4+x^5−x^6+x^8→不適

[7]

  Q(x)=x(x^2+1)(x^2+x+1)(x^2−x+1)=x+2x^3+2x^5+x^7→6面体サイコロ{1,3,3,5,5,7}

  R(x)=(x+1)(x^4−x^2+1)=1+x−x^2−x^3+x^4+x^5→不適

[8]

  Q(x)=x(x^2+1)(x^2+x+1)(x^4−x^2+1)=x+x^2+x^3+x^7+x^8+x^9→6面体サイコロ{1,2,3,7,8,9}

  R(x)=(x+1)(x^2−x+1)=x^3+1→2面体サイコロ{0,3}

[9]

  Q(x)=x(x^2+1)(x^2−x+1)(x^4−x^2+1)=x−2x^2+2x^3+x^4−x^5+x^7−x^8+x^9→不適

[10]

  Q(x)=x(x^2+x+1)(x^2−x+1)(x^4−x^2+1)=x+x^5+x^9→3面体サイコロ{1,5,9}

  R(x)=(x+1)(x^2+1)=1+x+x^2+x^3→4面体サイコロ{0,1,2,3}

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