132 (number) explained

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.^[1] With twelve divisors total where 12 is one of them, 132 is the 20th refactorable number, preceding the triangular 136.^[2]

132 is an oblong number, as the product of 11 and 12^[3] whose sum instead yields the 9th prime number 23;^[4] on the other hand, 132 is the 99th composite number.^[5]

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

.

132 is the smallest number in decimal with this property,^[6] which is shared by 264, 396 and 35964 (see digit-reassembly number).^[7]

The number of irreducible trees with fifteen vertices is 132.^[8]

In a

toroidal board in the n–Queens problem, 132 is the count of non-attacking queens,^[9] with respective indicator of 19^[10] and multiplicity of 1444 = 38^{2 [11]} (where, 2 × 19 = 38).^[12]

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

132 is also:

• OGLE-TR-132 is a magnitude 15.72 star in the star fields of the constellation Carina
• 132 Aethra is a M-type main belt asteroid
• Sonnet 132 by William Shakespeare
• The number of columns of a line printer printing in landscape mode on 14-inch paper.
• Refers to the Yo Soy 132 movement to vote in 2012 Mexican elections against PRI candidate Enrique Peña Nieto.

See also

• The year AD 132 or 132 BC
• List of highways numbered 132

References

1. Web site: Sloane's A000108 : Catalan numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-05-27.
2. 2024-03-12 .
3. 2024-03-12 .
4. 2024-03-12 .
5. 2024-03-12 .
6. Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 138
7. Numbers n equal to the sum of all numbers created from permutations of d digits sampled from n.
8. 2023-09-02 .
9. 2024-02-10 .
10. 2024-02-10 .
11. 2024-02-10 .
12. 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.