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Results tagged with co.combinatorics
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user 5010
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
9
votes
Accepted
How many edge-disjoint paths go from upper left to lower right in a $4 \times N$ rectangular...
To amplify on Christian's answer, the problem on a $K \times N$ grid for fixed $K$ and varying $N$ admits a finite-state transition model, so in particular is given by a linear recurrence.
The key is …
- 10.1k
12
votes
0
answers
261
views
Computing the number of ways to delete vertices sequentially without disconnecting a graph
Given a finite connected graph on $n$ vertices, we are trying to count the number of ways to label the vertices $1$ to $n$ so that deleting them sequentially in that order never disconnects the graph. …
- 10.1k
3
votes
characterization of regular languages among (say) those computable in linear time
(Answering Lukasz's question from the comments)
If you consider the non-commutative power series for a language, the regular languages are characterized by having rational power series constructable …
- 10.1k
1
vote
If the series Σ pᵃ⁽ʷ⁾·xᴵʷᴵ is rational, is Σ a(w)·xᴵʷᴵ also rational (summation over words ...
If there are only finitely many values for the $a_i$, then I believe the answer to both questions is affirmative for somewhat silly reasons. If you have any rational power series $f(x)$ with only fi …
- 10.1k