132_(number)

132 (number)

132 (number)

Natural number


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

Quick Facts ← 131 132 133 →, Cardinal ...

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 = 382 [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:

See also


References

  1. "Sloane's A000108 : Catalan numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
  2. Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 138
  3. 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. doi:10.1080/00029890.1994.11997004 JSTOR 2974691

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