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Tagged with bell-numbers combinatorial-proofs
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$F(n)$ is number of ways to partition set of $n$ without singleton blocks. Prove that $B(n) = F(n) + F(n+1)$
In this case $B(n)$ is $n$-th Bell number.
To be honest, I would really love to know if there is a combinatorial proof for that. If there is not, other proofs are appreciated too.
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Constructing a bijection to show that the number of equivalence relations on a finite set is equal to the bell numbers.
It is said that the Bell numbers count the number of partitions of a finite set. How can we prove that what they count is actually the number of partitions? I don't want to take it as a definition; I ...
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Combinatorial proof for Touchard's congruence
Bell number denoted $B_n$ is the number of ways to partition a set with cardinality $n$ into $k$ indistinguishable sets , where $0\le k\le n$
It's known that Bell numbers obey Touchard's Congruence ...
user715522
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Partitions of a set with n elements (proof)
I was reading a textbook about combinatorial mathematic which claimed that we can calculate the exact possible partitions of a set with n elements .
I searched it on wikipedia and I read about bell ...
user668140