Tootfinder

An exceptional equinumerosity of lattice paths and Young tableaux
Liam Ayres, Evan Bialo, Aidan Cook, Alwin Chen, Matteus Froese, Erica Liu, Maryam Mohammadi Yekta, Oliver Pechenik, Benjamin Wong
https://arxiv.org/abs/2506.03116

An exceptional equinumerosity of lattice paths and Young tableaux
We consider families $\mathcal{P}_n$ of plane lattice paths enumerated by Guy, Krattenthaler, and Sagan (1992). We show by explicit bijection that these families are equinumerous with the set $\mathrm{SYT}(n+2,2,1^n)$ of standard Young tableaux.

"In order to make an apple pie from scratch, you must first create the
universe."
-- Carl Sagan, Cosmos

The superspace coinvariant ring of type B
Sutanay Bhattacharya
https://arxiv.org/abs/2505.24122 https://arxiv.org/pdf/2505.24122

The superspace coinvariant ring of type B
Given the rank $n$ superspace $Ω_n$, the ring of polynomial-valued differential forms on $\mathbb C^n$, one can define an action of hyperoctahedral group $\mathfrak B_n$ on it. This leads to a superspace coinvariant ideal $SR_n^B$, defined as the quotient of $Ω_n$ by two-sided ideal generated by all $\mathfrak B_n$ invariants with vanishing constant terms. We derive the Hilbert series of $SR^B_n$ conjectured by Sagan and Swanson, and prove an operator theorem that yields a concrete descriptio…