132 (one hundred
ndthirty-two) is the
natural number
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive in ...
following
131 and preceding
133. It is 11
dozens.
In mathematics
132 is the sixth
Catalan number
The Catalan numbers are a sequence of natural numbers that occur in various Enumeration, counting problems, often involving recursion, recursively defined objects. They are named after Eugène Charles Catalan, Eugène Catalan, though they were p ...
. With twelve divisors total where 12 is one of them, 132 is the 20th
refactorable number, preceding the
triangular
A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called ''vertices'', are zero-dimensional points while the sides connecting them, also called ''edges'', are one-dimensional ...
136 136 may refer to:
*136 (number)
*AD 136
*136 BC
*136 (MBTA bus), a Massachusetts Bay Transportation Authority bus route
*136 Austria
136 Austria is a main-belt asteroid that was found by the prolific asteroid discoverer Johann Palisa on 18 Ma ...
.
132 is an
oblong number, as the product of 11 and 12 whose sum instead yields the 9th
prime number
A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...
23; on the other hand, 132 is the 99th
composite number
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Accordingly it is a positive integer that has at least one divisor other than 1 and itself. Every positive integer is composite, prime numb ...
.
Adding all two-
digit permutation
In mathematics, a permutation of a set can mean one of two different things:
* an arrangement of its members in a sequence or linear order, or
* the act or process of changing the linear order of an ordered set.
An example of the first mean ...
subsets of 132 yields the same number:
:
.
132 is the smallest number in
decimal
The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers (''decimal fractions'') of th ...
with this property, which is shared by
264
__NOTOC__
Year 264 (Roman numerals, CCLXIV) was a leap year starting on Friday of the Julian calendar. At the time, it was known as the Year of the Consulship of Gallienus and Saturninus (or, less frequently, year 1017 ''Ab urbe condita''). The ...
, 396 and 35964 (see
digit-reassembly number).
The number of
irreducible trees with fifteen
vertices is 132.
In a
toroidal board in the
''n''–Queens problem, 132 is the
count
Count (feminine: countess) is a historical title of nobility in certain European countries, varying in relative status, generally of middling rank in the hierarchy of nobility. Pine, L. G. ''Titles: How the King Became His Majesty''. New York: ...
of non-attacking queens, with respective
indicator
Indicator may refer to:
Biology
* Environmental indicator of environmental health (pressures, conditions and responses)
* Ecological indicator of ecosystem health (ecological processes)
* Health indicator, which is used to describe the health o ...
of
19 and
multiplicity of
1444 =
382 (where, 2 × 19 = 38).
[I. Rivin, I. Vardi and P. Zimmermann (1994)]
The n-queens problem.
American Mathematical Monthly
''The American Mathematical Monthly'' is a peer-reviewed scientific journal of mathematics. It was established by Benjamin Finkel in 1894 and is published by Taylor & Francis on behalf of the Mathematical Association of America. It is an exposi ...
. Washington, D.C.: Mathematical Association of America
The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university
A university () is an educational institution, institution of tertiary edu ...
. 101 (7): 629–639.
The exceptional
outer automorphism
In mathematics, the outer automorphism group of a group, , is the quotient, , where is the automorphism group of and ) is the subgroup consisting of inner automorphisms. The outer automorphism group is usually denoted . If is trivial and has a ...
of
symmetric group
In abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the composition of functions. In particular, the finite symmetric grou ...
''S''
6 uniquely maps vertices to factorizations and
edges to partitions in the
graph factors of the
complete graph
In the mathematical field of graph theory, a complete graph is a simple undirected graph in which every pair of distinct vertices is connected by a unique edge. A complete digraph is a directed graph in which every pair of distinct vertices i ...
with six vertices (and fifteen edges) ''K''
6, which yields 132
blocks in
Steiner system
250px, thumbnail, The Fano plane is a Steiner triple system S(2,3,7). The blocks are the 7 lines, each containing 3 points. Every pair of points belongs to a unique line.
In combinatorial mathematics, a Steiner system (named after Jakob Steiner ...
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
Enrique Peña Nieto (; born 20 July 1966), commonly referred to by his initials EPN, is a Mexican former politician and lawyer who was the 64th president of Mexico from 2012 to 2018. A member of the Institutional Revolutionary Party (PRI), he p ...
.
References
{{DEFAULTSORT:132 (Number)
Integers