All Questions
4
questions
1
vote
1
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101
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On $(0,1)$-strings and counting
Consider a binary string of length $n$ that starts with a $1$ and ends in a $0$. Clearly there are $2^{n-2}$ such bit strings. I would like to condition these sequences by insisting that the number of ...
- 339
0
votes
0
answers
60
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Books for developing an intuitive understanding of the partitions of numbers
I understand from the fundamental theorem of arithmetic that every number can be written as a product of its prime factors,but I’m curious about partitions,how numbers can be broken up into sums and ...
0
votes
1
answer
55
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Inequality relying on integer partitions and dominance ordering
Let $\lambda$, $\mu$ be two partitions of a natural number $n$, such that $\lambda$ dominates $\mu$ in the usual dominance order on partitions.
I would like to prove that if $q\geq 2$ is a natural ...
- 488
2
votes
0
answers
184
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Partitions and divisor functions: what is known about their relations?
If $i\geq 1$ is an integer, we have the following integer valued functions (for any integer $n\geq 0$):
\begin{align}
p_i(n)&=\textrm{the number of }i\textrm{-dimensional partitions of }n,\notag\\...
- 14.2k