132 (number)

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← 131 132 133 →
Cardinal one hundred thirty-two
Ordinal 132nd
(one hundred thirty-second)
Factorization 22 × 3 × 11
Divisors 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132
Greek numeral ΡΛΒ´
Roman numeral CXXXII, cxxxii
Binary 100001002
Ternary 112203
Senary 3406
Octal 2048
Duodecimal B012
Hexadecimal 8416

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

Contents

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

References

  1. ↑ "Sloane's A000108 : Catalan numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
  2. ↑ Sloane, N. J. A. (ed.). "SequenceA033950(Refactorable numbers: number of divisors of k divides k. Also known as tau numbers.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-03-12.
  3. ↑ Sloane, N. J. A. (ed.). "SequenceA002378(Oblong (or promic, pronic, or heteromecic) numbers: a(n) equal to n*(n+1).)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-03-12.
  4. ↑ Sloane, N. J. A. (ed.). "SequenceA000040(The prime numbers.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-03-12.
  5. ↑ Sloane, N. J. A. (ed.). "SequenceA002808(The composite numbers.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-03-12.
  6. ↑ Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 138
  7. ↑ Sloane, N. J. A. (ed.). "SequenceA241754(Numbers n equal to the sum of all numbers created from permutations of d digits sampled from n)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  8. ↑ Sloane, N. J. A. (ed.). "SequenceA000014(Number of series-reduced trees with n nodes.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-09-02.
  9. ↑ Sloane, N. J. A. (ed.). "SequenceA054502(Counting sequence for classification of nonattacking queens on n X n toroidal board.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-02-10.
  10. ↑ Sloane, N. J. A. (ed.). "SequenceA054500(Indicator sequence for classification of nonattacking queens on n X n toroidal board.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-02-10.
  11. ↑ Sloane, N. J. A. (ed.). "SequenceA054501(Multiplicity sequence for classification of nonattacking queens on n X n toroidal board.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 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. doi : 10.1080/00029890.1994.11997004 JSTOR   2974691
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