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Shroudmaster
@shroudmaster1.bsky.social

Is there a reason for the quotes in alphabetical order? I find students sometimes find quotes confusing, and the example never really breaks from lexicographical order. Was it just to avoid defining lexicographical order?

ꭓle Ormsby 𓆙
@e-infinity.space

Yes! My students learn that first as an application of 'additive counting' — partition the 2ⁿ subsets of an n-element set by cardinality — and they see the algebraic proof later. Then I make them decide which proof they like better :)

ꭓle Ormsby 𓆙
@e-infinity.space

Do you know a good way to package G-sets of the form (G/H choose k) with Tamara functors? I think I can compute their ghost coordinates, but I don’t find the resulting formulae very satisfying.

Yuri Sulyma
@yurisulyma.bsky.social

What do you mean by the ghost coordinates of a G-set? The orbit decomposition? If R is a Green functor, you can define ideals I_H = fib(R^G → R^H) (If R doesn't have surjective restrictions then I_H is a "quasi-ideal" i.e. a derived thing.) Then you can let (n)_R! := ⊗_{|H| ≤ n} I_H

ꭓle Ormsby 𓆙
@e-infinity.space

Ghost coordinates = table of marks, so number of fixed points with respect to each conjugacy class of subgroup. You can recover orbit decomposition from ghost coordinates.

Yuri Sulyma
@yurisulyma.bsky.social

For G=𝕋, this recovers (the ideal generated by) (n)_q! for [H ↦ π₀ ku^tH ] and (q-1)^n (n)_q! for [H ↦ π₀ ku^hH]. Note that here I_{C_n} = π_{λ^n}, using the cell structure 𝕋/C_n → S⁰ → S^{λ^n} and λ⁰ + … + λ^{n-1} = Ind^{C_n}_e(ℂ); this is related to the slice filtration. Idk if that helps