132 (number)

132 (one hundred [and] thirty-two) is the natural number following 131 and preceding 133. It is 11 dozens.

In mathematics

132 is the sixth Catalan number.<ref>Template:Cite web</ref> With twelve divisors total where 12 is one of them, 132 is the 20th refactorable number, preceding the triangular 136.<ref>Template:Cite OEIS</ref>

132 is an oblong number, as the product of 11 and 12<ref>Template:Cite OEIS</ref> whose sum instead yields the 9th prime number 23;<ref>Template:Cite OEIS</ref> on the other hand, 132 is the 99th composite number.<ref>Template:Cite OEIS</ref>

Adding all two-digit permutation subsets of 132 yields the same number:

<math>12 + 13 + 21 + 23 + 31 + 32 = 132</math>.

132 is the smallest number in decimal with this property,<ref>Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 138</ref> which is shared by 264, 396 and 35964 (see digit-reassembly number).<ref>Template:Cite OEIS</ref>

The number of irreducible trees with fifteen vertices is 132.<ref>Template:Cite OEIS</ref>

In a <math>15 \times 15</math> toroidal board in the n–Queens problem, 132 is the count of non-attacking queens,<ref>Template:Cite OEIS</ref> with respective indicator of 19<ref>Template:Cite OEIS</ref> and multiplicity of 1444 = 38² <ref>Template:Cite OEIS</ref> (where, 2 × 19 = 38).<ref>I. Rivin, I. Vardi and P. Zimmermann (1994). The n-queens problem. American Mathematical Monthly. Washington, D.C.: Mathematical Association of America. 101 (7): 629–639. Template:Doi Template:JSTOR</ref>

The exceptional outer automorphism of symmetric group S₆ uniquely maps vertices to factorizations and edges to partitions in the graph factors of the complete graph with six vertices (and fifteen edges) K₆, which yields 132 blocks in Steiner system S(5,6,12).

In other fields

• Refers to the Yo Soy 132 movement to vote in 2012 Mexican elections against PRI candidate Enrique Peña Nieto.

References

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