issue with randomAbstractSimplicialComplex(n,m,d)

[mahrud]

The documentation says randomAbstractSimplicialComplex(n,m,d) will:

Create the random complex $Y_d(n,m)$ which has vertex set $[n]$ and complete $(d − 1)$-skeleton, and has exactly m d-dimensional faces,

But it seems like some complexes produced this way have fewer than $m$ faces of dimension $d$:

i28 : tally apply(1000, i -> length facets randomAbstractSimplicialComplex(5,3,2))

o28 = Tally{1 => 7  }
            2 => 272
            3 => 721

(This is from Example 4.1 of the paper, which seems to have the same issue.)

Further, even among the ones that satisfy the previous criterion, unless I'm misunderstanding something, the $d-1$-skeletons don't appear to be complete:

i30 : L = apply(1000, i -> randomAbstractSimplicialComplex(5,3,2));

i31 : L = select(L, C -> 3 == length facets C);

i32 : #L

o32 = 746

i33 : tally apply(L, C -> length C#1)

o33 = Tally{6 => 109}
            7 => 437
            8 => 200

Are these bugs? Perhaps the documentation should be corrected to say the result isn't guaranteed.

(ps: this wasn't discovered by me but the person didn't want to be involved)

[n-m-g]

Hi, Many thanks. I can provide a small clarification to the documentation as you suggest. Best, Nathan

…

On May 14, 2025, at 11:26 AM, Mahrud Sayrafi ***@***.***> wrote: mahrud created an issue (Macaulay2/M2#3818) <#3818> The documentation says randomAbstractSimplicialComplex(n,m,d) will: Create the random complex $Y_d(n,m)$ which has vertex set $[n]$ and complete $(d − 1)$-skeleton, and has exactly m d-dimensional faces, But it seems like some complexes produced this way have fewer than $m$ faces of dimension $d$: i28 : tally apply(1000, i -> length facets randomAbstractSimplicialComplex(5,3,2)) o28 = Tally{1 => 7 } 2 => 272 3 => 721 (This is from Example 4.1 of the paper.) Further, even among the ones that satisfy the previous criterion, unless I'm misunderstanding something, the $d-1$-skeletons don't appear to be complete: i30 : L = apply(1000, i -> randomAbstractSimplicialComplex(5,3,2)); i31 : L = select(L, C -> 3 == length facets C); i32 : #L o32 = 746 i33 : tally apply(L, C -> length C#1) o33 = Tally{6 => 109} 7 => 437 8 => 200 Are these bugs? Perhaps the documentation should be corrected to say the result isn't guaranteed. (ps: this wasn't discovered by me but the person didn't want to be involved) — Reply to this email directly, view it on GitHub <#3818>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/ABC62JFURCHHMSPCGT2E5QL26NOBZAVCNFSM6AAAAAB5DWOU7SVHI2DSMVQWIX3LMV43ASLTON2WKOZTGA3DGNJRGE4DONQ>. You are receiving this because you were assigned.

[n-m-g]

Hi, I’ve pushed these small clarifications now. Do let me know if there is anything else. Best, Nathan

…

On May 14, 2025, at 11:38 AM, Nathan Grieve ***@***.***> wrote: Hi, Many thanks. I can provide a small clarification to the documentation as you suggest. Best, Nathan > On May 14, 2025, at 11:26 AM, Mahrud Sayrafi ***@***.***> wrote: > > > mahrud > created an issue > (Macaulay2/M2#3818) > <#3818> > The documentation says randomAbstractSimplicialComplex(n,m,d) will: > > Create the random complex $Y_d(n,m)$ which has vertex set $[n]$ and complete $(d − 1)$-skeleton, and has exactly m d-dimensional faces, > > But it seems like some complexes produced this way have fewer than $m$ faces of dimension $d$: > > i28 : tally apply(1000, i -> length facets randomAbstractSimplicialComplex(5,3,2)) > > o28 = Tally{1 => 7 } > 2 => 272 > 3 => 721 > (This is from Example 4.1 of the paper.) > > Further, even among the ones that satisfy the previous criterion, unless I'm misunderstanding something, the $d-1$-skeletons don't appear to be complete: > > i30 : L = apply(1000, i -> randomAbstractSimplicialComplex(5,3,2)); > > i31 : L = select(L, C -> 3 == length facets C); > > i32 : #L > > o32 = 746 > > i33 : tally apply(L, C -> length C#1) > > o33 = Tally{6 => 109} > 7 => 437 > 8 => 200 > Are these bugs? Perhaps the documentation should be corrected to say the result isn't guaranteed. > > (ps: this wasn't discovered by me but the person didn't want to be involved) > > — > Reply to this email directly, view it on GitHub <#3818>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/ABC62JFURCHHMSPCGT2E5QL26NOBZAVCNFSM6AAAAAB5DWOU7SVHI2DSMVQWIX3LMV43ASLTON2WKOZTGA3DGNJRGE4DONQ>. > You are receiving this because you were assigned. >

[n-m-g]

As a final comment about this for now, perhaps the best approach would be to create an option that allows for both the complete and not complete skeleton cases. I will think about adding that capability at a future time. In either case, it is good to have the more general case for now. Do let me know if there is anything else.

[n-m-g]

Oh, one other thing. I guess I could add a small sentence or two to the documentation defining what is meant by complete skeleton for the purpose of the package as well. That might have clarified the original question too. Many thanks for asking about this.

[n-m-g]

I've actually just added options to the method now to treat the two different cases (and hopefully to clarify everything). Let's see if it compiles OK.

[n-m-g]

Hi,

This new functionality has been implemented in the pull request @ #3821

Please close this "issue". Many thanks.

Best,
Nathan

[n-m-g]

As I've mentioned this "issue" as been resolved and new functionality has been added to the method. (There is no "issue" with the code.). Please close this issue thread.