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Results tagged with co.combinatorics
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user 65801
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
2
votes
Number of prime divisors with multiplicity in a sum of Gaussian binomial coefficients
Here is an example (I hope I did this right!): With $t=5$ I get $a_5^q=2 q^6+2 q^5+6 q^4+6 q^3+6 q^2+4 q+6$. In particular $a_5^q+1\geq q^{5+1}$ for any prime $q$. Letting $q=79$ we get $a_5^q+1 = 492 …
- 1,907
3
votes
Accepted
Probability that k randomly drawn permutations can be arranged to compose to the identity
Only a partial answer, which however is too long for a comment: Let $p_{n,k}$ denote the given probability. Then we have
(1) $p_{n,1} = p_{n,2} = \frac{1}{n!}$, $p_{n,3} = \frac{2\cdot n!-p(n)}{(n!)^2 …
- 1,907
11
votes
Accepted
Show a sequence of sums involving Catalan Numbers converges
By 'magic' and a computer (see the book "A=B" by Petkovsek, Wilf and Zeilberger https://www.math.upenn.edu/~wilf/AeqB.html) the numbers $\mathcal{E}_s$ satisfies the recurrence
$\sum_{k=0}^3 P_k(s) \m …
- 1,907