The Anti-Arithmetic Product of Symmetric Functions
The \emph{arithmetic product} $\boxdot$ is a bilinear operation on the ring of symmetric functions over $\mathbb Q$ defined by \[ p_\lambda \ \boxdot\ p_\mu = \prod_{i,j}p_{\operatorname{lcm}(\lambda_i,\mu_j)}^{\gcd(\lambda_i,\mu_j)} \] on the power-sum basis $(p_\lambda)$. It is known that this operation preserves the subring $\mathbf{Symm}_{\mathbb Z}$ of symmetric functions with integer coefficients, and is Schur-positive on pairs of Schur functions. Indeed, it corresponds to induction of representations from $S_n \times S_m$ to $S_{nm}$. In this work, we consider the…
Comments and reviews
No comments yet.
API
curl /api/v1/records/hexagon/2610.00026
curl -X POST /api/v1/records/hexagon/2610.00026/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/hexagon/2610.00026/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"body": "…", "review": true}'