darij grinberg

This is an instance of the identity $\sum\limits_{k=1}^n k \dbinom{n+1}{k+1} x^{n-k} = \left(n-x\right)\left(1+x\right)^n + x^{n+1}$, which holds for any number $x$. Various proofs are possible, e.g., by rewriting the factor $k$ on the left hand side as $\left(k+1\right)-1$. I wouldn't go looking for a combinatorial proof that works only for one value of $x$.

then your \sum_{\pi} part multiplies this by an additional column symmetrizer b_t

so you get a_t * read(t), where a_t is the row symmetrizer of t

ok, it is r*read(t)

or maybe read(t)*r

in order to embed the tabloid module into the group algebra, you have to send each tabloid {t} to the sum of r*read(t) over all row-permutations of t (where read(t) is the reading word of t in a specified reading order)

haha he doesn't even mention the ideal definition

Definition 2.5 is the polytabloid definition

ma.rhul.ac.uk/~uvah099/Maths/Sym/SymGroup2014.pdf

i'd look at wildon's notes for a quick definition

does she define them?

i think these are equivalent

or by polytabloids in the tabloid module

either as the ideal generated by "row symmetrizer times column symmetrizer" in the symmetric group algebra

nah, they can be defined over any commutative ring

IMHO even the existence of a $\ZZ$-module basis is unknown

i'd love to hear some more results about them

yeah the specht_module class is for bad shapes, as in dspace.mit.edu/handle/1721.1/60196

if you have the time, would be worth looking at the yang-baxter construction of the specht rep, and check if it gives integer entries

its main purpose is to cover arbitrary diagrams (not just partitions)

it's very slow

keep in mind that this is a toy implementation of the definition with no tricks and shortcuts

ah yes, this is recent enough (note the 2023 year in the documentation)

Ah, right, specht_module works over any field (not sure how I had forgotten it, as I was the one reviewing that ticket IIRC). What exactly does not work?

@JacksonWalters: As long as the basis is a $\mathbb Z$-basis, this is true. Is it for the Sage implementation? I'd hope but I don't know.

@JacksonWalters: Please be aware that the only currently supported implementations of Specht modules in Sage are "seminormal", "orthogonal" and "Specht", and (to my knowledge) all of them are written in a way that presupposes at least characteristic $0$. (A pity if you ask me: at least Specht should know better...)

PS. Auditing students shouldn't affect a curve anyway, should they? If they do, IMHO that's another problem worth fixing.

You've rightfully called the students in question "clowns". If you can get this attitude across to your colleagues teaching the other sections as well as the best of your students, the clown circus will have to move out of town, because being widely seen as a clown does not make one popular with girls.

I don't know the details of your situation, but it sounds to me like a problem that should be addressed at its branches, not its roots: discipline/expel the actual harassers (contact the TIX office when you hear serious complaints); give the rest a public heads-up that they're mostly wasting time and their peacockery isn't necessarily making them popular (here you should get your colleagues on board: status is an echo chamber); make sure there isn't such a shortage of actual tutors that anyone has to rely on this unofficial help; and for hell's sake, stop curving down the exams.

Does it matter much that the student sex statistics are published? I can easily imagine the app designers got the idea from these numbers, but IMHO you don't need fine-grained data to know that life science majors skew female and consequently the service courses that are required for them will create, uhm, opportunities. Having numbers is just making the targeting a bit more precise.

@BryanKrause: Is it the part where he wants to keep publishing on his subject? Most professional academics would.

@BryanKrause: There is at least one ongoing case of a Russian nuclear physicist/engineer whistleblowing to gulagu.net; it's "more likely than you think", as the old meme says.

@ElizabethHenning: I'm not exactly writing a paper here; nor are you. But a post like the above, which is telling minorities to avoid showing any personality because everyone around is aiming at their necks, would need some good evidence that would probably show up in a google search like the one I did. Note that your claim that "in-groups get cut way more slack than out-groups" is much weaker than the one the post is making; I wouldn't be surprised if some studies confirm it, particularly when it comes to things like gaps in the CV. However, that's not xLeitix's claim!

... no literature whatsoever. Short of that, anecdotes? I'd be happy to hear some, but no one is telling!

... recent paper, again not specific to the academic job market, that finds a penalty for women that show "gender-incogruent" behavior on their CV (e.g., male-typical hobbies), and surprisingly a (slight) reward for men in the mirror scenario. That said, it relies on some predictive modeling magic rather than on actual reviewers; I'm not quite sure how much to think of it. In either case, I see very little that would apply to photography (which is maybe slightly female-coded) as a hobby. On the academic job market, I can find ...

@ElizabethHenning: There's a saying that anything stated without evidence can be dismissed without evidence. But let's actually look at the literature. The most relevant source I can find is a masters thesis by Kateryna Hunko from Linz which is concerned with non-academic hiring and finds a minor gender difference that flips depending on the type of hobby and the criteria applied. Then there is a ...

I'm asking for evidence of a claim you're making about academic hiring process, not of your academia.SE experience. As it stands, you are giving rather radical advice to minorities -- one that will likely damage their social life, because keeping your hobbies visible lets you meet friends -- on questionable factual footing.

Do you have any data on the minority relation, or is it just a guess?

@IanSudbery: "colonisation is when one people, polity or culture exerts power over another to replace the people, polity or culture and so make the colonising people, polity or culture the de facto norm" Nice characterization of the last 12 years of Democrat politics :)

@IanSudbery (next comment): "why so few BAME students apply to our courses" has as many explanations as there are people suggesting explanations. Very little is understood about disparities in career choices; we haven't even figured out the gender-equality paradox ( en.wikipedia.org/wiki/Gender-equality_paradox ). At this point, it's a Rorschach test more than a scientific question. On a DEI committee, I assume it will come down to racism, but that's about how these committees tick.

... From what I have seen on the "decolonial" side of the discourse, these issues are ignored entirely.)

... As to the issues with "genetic resources" (not quite sure which ones you are talking about), what does this imply for curricula? (These issues can be deeply non-straightforward; it is far from clear how to benefit a third world country that is governed by a hopelessly corrupt regime and/or in danger of societal collapse. What happened to the Mesopotamian archaeological finds returned to Iraq when ISIS came into town? ...

@IanSudbery: All examples are coming from biology in the wide sense, as I expected :) And the focus on first world diseases is indeed one thing where widening the course offerings is a good idea. But there is not really a scientific or moral necessity for it -- it's perfectly fine to argue that a university in a given country can choose to focus on the issues most prevalent in said country. It's just less of a wide focus than one could hope for. ...

@BryanKrause: Disparities start long before undergraduate admissions and are multifactorial. Why should curricula be the right lever to pull? (And it's absolutely weird to speak of colonialism when you are talking about things happening contemporarily.)

@BryanKrause: Very little of this is relevant to STEM curricula. (I can think of some relevance in medicine, but it is probably better put into a different frame.)

... that Diego de Landa has burned, nor to recover the lost books of the library of Baghdad. Trying to fill the gaps with "oral history" and activist speculation is no better than seeking cosmological constants in the dimensions of the Great Pyramid. As to the content of Western science, thousands of researchers from all over the globe easily joining its tradition (well, no less easily than us Westerners do so) are reason enough for me to believe its objectivity.

@JSLavertu: I have assumed that the OP is about STEM, even though it has been left unsaid. I do not want to claim too much about the humanities as there is a rather wide variety. In STEM, I stand to the claim that "colonialism" (even in the widest senses) is not embedded in the current curriculum to any extent that would warrant urgent removal (or "decolonization"). The fact that the history of Western science is better known than many parallel developments is well-understood, and has been so for decades, but unfortunately there is no way to unburn the manuscripts ...

It is indeed rather "arrogant to propose that we can" remove something that is not there.

... interests to the current decade's buzzwords (which happens far too often, but no one on academia.stackexchange would defend). So, no, it is not "how you will do your job well", no more than a physicist's "doing their job well" should include writing breathless grant proposals about deep learning and climate change.

@AnonymousPhysicist: An academic job is first and foremost about research, then about teaching, and finally about service, which can include many things from founding clubs through making expository videos to maintaining free software. On each of the three, we traditionally trust the academic to choose their path and merely see that something interesting and useful comes out in the end (scientific freedom). Expecting researchers to adapt their service interests to a narrow (if hyped to a fault) segment of contemporary politics is no better than expecting them to adapt their research ...