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Results tagged with co.combinatorics
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user 961
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
5
votes
Is the "diagonal" of a regular language always context-free?
It's unnecessary to assume that L is unambiguous: a regular language always is, because there exists a DFA that accepts it.
Following Richard's notation, it is easy to construct a DPDA for K, so it i …
- 1,015
4
votes
3
answers
662
views
Minimum cover of partitions of a set
Given $n,k\in\mathbb{N}$ where $k\leq n$, I want to compute the minimum subset of the set of partitions of $N$={$1,\ldots,n$}, satisfying these properties:
Each block of every partition has at most …
- 1,015
31
votes
Accepted
Exhibit an explicit bijection between irreducible polynomials over finite fields and Lyndon ...
In Reutenauer's "Free Lie Algebras", section 7.6.2:
A direct bijection between primitive necklaces of length $n$ over $F$ and the set of irreducible polynomials of degree $n$ in $F[x]$ may be describe …
- 1,015
1
vote
How to compute the rook polynomial of a Ferrers board?
Although the closed formula is what I wanted, a dynamic programming approach behaves better algorithmically:
Define $M_{i,j}$ as the number of ways to place $j$ non-attacking rooks on the Ferrers boa …
- 1,015
4
votes
2
answers
2k
views
How to compute the rook polynomial of a Ferrers board?
Given a Ferrers board of shape $(b_1,\ldots,b_m)$, we define $r_k$ as number of ways to place $k$ non-attacking rooks (as in Chess). In section 2.4 of Stanley's Enumerative Combinatorics (vol. 1) it's …
- 1,015
14
votes
0
answers
4k
views
Minimum tiling of a rectangle by squares
Given the $n\times m$ rectangle, I want to compute the minimum number of integer-sided squares needed to tile it (possibly of different sizes).
Is there an efficient way to calculate this?
- 1,015