Math Problem Statement
Let
π
(
π
,
π
)
T(m,n) be the number of monotone functions
π
f from
[
π
]
[m] to
[
π
]
[n]. That is, functions
π
:
[
π
]
β
[
π
]
f:[m]β[n] such that
1
β€
π
β€
π
β€
π
1β€iβ€jβ€m implies
π
(
π
)
β€
π
(
π
)
f(i)β€f(j). What is
π
(
10
,
2
)
T(10,2)?
Solution
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Math Problem Analysis
Mathematical Concepts
Combinatorics
Monotone Functions
Binomial Coefficients
Weakly Increasing Sequences
Formulas
T(m,n) = sum(binomial(m, k), k=0 to m)
2^m (for T(m, 2))
Theorems
Binomial Theorem
Weakly Increasing Sequence Theorem
Suitable Grade Level
Grades 9-12
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