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Apr
6 |
comment |
Missing citations of “to appear” papers on MathSciNet
The "to appear" articles usually don't have a MathSciNet entry associated with them yet. I read the linked webpage as saying that having e.g. an MR number assigned as being the deciding factor as to whether or not the citation is assigned correctly. |
Apr
6 |
answered | Missing citations of “to appear” papers on MathSciNet |
Apr
4 |
comment |
Positivity of the alternating sum of indices for boolean interval of finite groups
You might look at (4.1.1) of "Poset topology: tools and applications", by Michelle Wachs. That survey paper also explains why this holds. It is possible for a Cohen-Macaulay poset to have 0 as its Möbius number, for example if it is contractible. That's maybe another reason to use the EL-labeling machinery -- that gives you an explicit calculation for the Möbius number as the number of decreasing chains. See Theorem 3.2.4 of the same survey paper. |
Apr
4 |
comment |
Positivity of the alternating sum of indices for boolean interval of finite groups
The main point is that the Möbius number of a poset is an Euler characteristic of the associated order complex. See en.wikipedia.org/wiki/Poset_topology . |
Apr
4 |
comment |
Positivity of the alternating sum of indices for boolean interval of finite groups
There are lots of ways to prove a complex to be Cohen-Macaulay. Actually, you only need for the order complex to have the homology of a bouquet of spheres in a fixed dimension with the right parity. I edited the post for clarity. |
Apr
4 |
revised |
Positivity of the alternating sum of indices for boolean interval of finite groups
edited for clarity, following comment/question of original author |
Apr
3 |
awarded | Revival |
Apr
2 |
answered | Positivity of the alternating sum of indices for boolean interval of finite groups |
Apr
1 |
answered | Generating finite simple groups with $2$ elements |
Feb
15 |
comment |
List of counting proofs instead of linear algebra method in combinatorics
Is it possible that there might be some kind of shifting-type proof of Oddtown? |
Jan
15 |
awarded | Nice Answer |
Jan
4 |
comment |
Generalization of $(HK:H)=(K:H\cap K)$
As you might have already noticed, you don't need $H$ to normalize $K$ for (*) to hold, only for the two groups to permute setwise. |
Dec
8 |
answered | f vectors of simplicial complexes homeomorphic to n dimensional spheres |
Dec
4 |
awarded | Yearling |
Jul
14 |
awarded | Necromancer |
Jul
13 |
awarded | Revival |
Jul
13 |
comment |
Generating random finite groups
It's not clear to me that the procedure described above wouldn't favor certain isomorphism classes. The original question wanted an equal chance at each isomorphism class of groups of order $n$. |
Jul
13 |
comment |
Generating random finite groups
Indeed, GAP even knows the count of these groups with NumberSmallGroups (but it won't let you get at the groups themselves via the SmallGroups library). |
Jul
13 |
answered | Generating random finite groups |
May
15 |
answered | Is there a (satisfying) proof that cellular cohomology is isomorphic to simplicial cohomology that doesn't use relative cohomlogy? |