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Results tagged with co.combinatorics
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user 36466
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
3
votes
Help identify this generalized sign of real representations
I think the answer to your second question is "no". Note first that by the M\"obius inversion formula (see for example Chapter 3 of Richard Stanley's ``Enumerative Combinatorics, Volume 1"), for any …
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7
votes
Accepted
Vanishing homology of simplicial complexes with few facets
By the nerve lemma, your complex is homotopy equivalent to a complex with $n-t$ vertices and therefore has trivial homology in degrees greater than $n-t-2$
- 3,571
3
votes
Accepted
About the sum of rectangular power sums
Talking to Sheila Sundram, as suggested in the comments, was a good idea. After some conversation, the following proof became apparent. I don't know of any proof already in the literature.
Let $g$ b …
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9
votes
fixed points of permutation groups
Primitive actions of $S_n$ other than the natural one were examined by Diaconis, Fulman and Guralnick in ``On fixed points of permutations." J. Algebraic Combin. 28 (2008), no. 1, 189–218. The inter …
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47
votes
Accepted
5
votes
Field with one element look at counting index-$n$ subgroups in terms of Homs to $S_n$, gener...
Thomas M\"uller has done a very careful and thorough study of problems of this type. While I don't know that the formula you write is a special case of Theorem 1 in his paper ``Enumerating Representa …
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4
votes
Combinatorial Morse functions and random permutations
Please allow me to answer an amended question. It seems better to me to count discrete gradient flows instead of discrete Morse functions (of course this is a matter of opinion). In the case of the …
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7
votes
A general formula for the number of conjugacy classes of $\mathbb{S}_n \times \mathbb{S}_n$ ...
I don't know that it is of the type you wish, but there is a formula of sorts.
Consider the more general case of a finite group $G$ acting diagonally by conjugation on the set of $k$-tuples of elemen …
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3
votes
Accepted
Posets of finite sequences are highly connected
If I understand your question correctly, an answer should appear in the paper "On lexicographically shellable posets" of Anders Bj\"orner and Michelle Wachs, in Transactions of the AMS 277, pp. 323-34 …
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2
votes
Accepted
Combinatorial problem in $G(32, \, 6)$
Here is a proof by contradiction. Assume an $8$-tuple $E$ from $G$ satisfies all of your relations.
Let $\Phi=\langle w^2,x,y \rangle \leq G$. It is straightforward to observe that
(A) $\Phi$ is abel …
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17
votes
Accepted
The Möbius number of the nonabelian finite simple groups
The answer to your question is ``yes". Something more general was proved by Hawkes, Isaacs and \"Ozaydin in a 1989 paper in the Rocky Mountain Journal of Mathematics.
CORRECTION: As Sebastien Palcou …
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