All Questions
Tagged with combinatorics number-theory
275
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Given a finite group, does this equation involving group's order, a partition of it and centralizers' orders hold?_Attempt#2
After failing this attempt, I've revised my proof sketch and I've come to the following version of the equation in the title.
So, let $G$ be a finite group, say $G=\lbrace e,a_1,\dots,a_{n-1} \rbrace$...
user615081
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Complete Directed Graph Indegree and Outdegree summations
Let the indegree of a vertex $v$ be $i(v)$ and the outdegree be $o(v)$. Consider a single tournament (a directed graph obtained by assigning a direction for each edge in an undirected complete graph) ...
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Analysis of super-structures emerging in a spiral representation of prime numbers
The fact that each prime number (greater than $9$) ends with one of the four digits $1,3,7,9$, allows us to classify the tens in which the primes are found according to which of these four digits, ...
user559615
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Expected number of parts of a uniformly selected partition of $n$
I have a very basic question on partition theory, which I feel should be very well known. Suppose that you fix a natural number $n$ and select a random partition $P$ of $n$ by choosing uniformly from ...
- 469
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Maximizing sum of metric function on a set (Adaptation of Hungarian Algorithm)
Suppose I have a set of unique elements $A=\{a_1, a_2, ..., a_n\}$. Suppose I also have a metric function $f:A\times A \rightarrow R^+$. I want to choose $k$ elements from $A$ (i.e. $a_{i_1},a_{i_2}, ....
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