# Tagged Questions

Questions related to the different ways of expressing an integer as a sum of integers; or, questions related to the subdivision of a set into smaller disjoint sets; questions related to the subdivision of an interval into smaller intervals that intersect only at the endpoints.

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### Generating functions, Schur's identity

Let $S=\{n\in \mathbb{Z}_+ \mid n \equiv 1, 5 \,\,(\text{mod 6})\}.$ Let $a(n)$ be the number of partitions of $n$ into parts belonging to $S,$ and $b(n)$ be the number of partitions of $n$ into ...
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### Index set of dyadic partition

Imagine if you have a line from 0 to 1, and you begin partitioning it dyadically. The first point will be at 0, the second at 1 and the third at 0.5, the fourth at 0.25, the fifth at 0.75 etc. Let's ...
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### Is there a standard representation for the composition of an integer?

In the same way as "$\vdash$" represents integer partition, what would be the symbol for composition (ordered partition)?
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### How to find last digit of number of partitions?

Is there simpler way to find last digit or last k digits (in any base) of p(n) than calculating full number?
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### What is a Fixed Partition?

I have two partition, P= {$x_0,x_1,...,x_n$} and Q= {$y_0, y_1,...,y_n$}. P is a general partition of the interval of [a,b] and Q is a fixed partition of [a,b]. What does it mean for Q to be fixed? ...
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### Non-Uniform grid

Let say I have $v_0\in [v_1,v_m]$ (say $v_0=0.04\in [0.004,0.24]$) I would like to find a $1$-to-$1$ map that map $[0,1]$ to $[v_1,v_m]$ and more cluster points around $v_0$ from two sides. It seem ...
I've found that if there are $N$ objects split up into two groups of $n_1$, and $n_2=N-n_1$ then this can be divided into $$\frac{N!}{n_1!(N-n_1)!}$$ groups. How can I extend this onto splitting $N$ ...
### Understanding the definition of refinement of a partition $P$.
Definition. Let $P$, $P'$ be partitions at $[a,b]$. We say that $P'$ is a refinement of $P$ if $P'$ $\supseteq$ $P$. I did not understand really of the definition of refinement. Can you give me a ...