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132 (number)

FieldValue
number132
divisor1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132

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. With twelve divisors total where 12 is one of them, 132 is the 20th refactorable number, preceding the triangular 136.

132 is an oblong number, as the product of 11 and 12 whose sum instead yields the 9th prime number 23; on the other hand, 132 is the 99th composite number.

Adding all two-digit permutation subsets of 132 yields the same number: :12 + 13 + 21 + 23 + 31 + 32 = 132.

132 is the smallest number in decimal with this property, which is shared by 264, 396 and 35964 (see digit-reassembly number).

The number of irreducible trees with fifteen vertices is 132.

In a 15 \times 15 toroidal board in the n–Queens problem, 132 is the count of non-attacking queens, with respective indicator of 19 and multiplicity of 1444 = 382 (where, 2 × 19 = 38).

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

References

  1. "Sloane's A000108 : Catalan numbers". OEIS Foundation.
  2. {{Cite OEIS. A033950. Refactorable numbers: number of divisors of k divides k. Also known as tau numbers.
  3. {{Cite OEIS. A002378. Oblong (or promic, pronic, or heteromecic) numbers: a(n) equal to n*(n+1).
  4. {{Cite OEIS. A000040. The prime numbers.
  5. {{Cite OEIS. A002808. The composite numbers.
  6. Wells, D. ''[[The Penguin Dictionary of Curious and Interesting Numbers]]'' London: Penguin Group. (1987): 138
  7. {{Cite OEIS. A241754
  8. {{Cite OEIS. A000014. Number of series-reduced trees with n nodes.
  9. {{Cite OEIS. A054502. Counting sequence for classification of nonattacking queens on n X n toroidal board.
  10. {{Cite OEIS. A054500. Indicator sequence for classification of nonattacking queens on n X n toroidal board.
  11. {{Cite OEIS. A054501. Multiplicity sequence for classification of nonattacking queens on n X n toroidal board.
  12. I. Rivin, I. Vardi and P. Zimmermann (1994). [https://www.jstor.org/stable/2974691 The n-queens problem.] [[American Mathematical Monthly]]. Washington, D.C.: [[Mathematical Association of America]]. '''101''' (7): 629–639. {{doi. 10.1080/00029890.1994.11997004 {{JSTOR. 2974691
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