The conjecture concerns a determinantal expression for a related antisymmetrizer arising in the study of symmetric functions and alternating-sign-matrix enumeration. The supplied sources do not state the antisymmetrizer, its variables, or the proposed determinant explicitly, so a more precise quantified formulation cannot be recovered from them.

Conjectures of Colomo–Pronko and Lukas Riegler on antisymmetrizer determinant formulas

The problem concerns conjectures linking antisymmetrizer determinant identities with symmetric functions and alternating-sign-matrix enumeration. The recent preprint addresses conjectures attributed to Colomo–Pronko and Lukas Riegler, but its supplied metadata does not identify the contributors.

Known results

Aigner, Fischer, Konvalinka, Nadeau, and Tewari, 2020: proved a new antisymmetrizer-to-determinant formula and a Schur-polynomial expansion conjectured independently by two groups.
The same work connected these functions with refined enumeration of alternating-sign matrices.

August 2026 preprint

The preprint proves a new determinantal identity for an antisymmetrizer and uses it to claim one named conjecture, apparently the Riegler conjecture. It also formulates a related version of the Colomo–Pronko conjecture without claiming its full proof; these claims remain unverified.

Current status (as of August 2026): A claimed advance and claimed proof of one related conjecture are unverified, while the full Colomo–Pronko conjecture remains open.

Conjectures of Colomo–Pronko and Lukas Riegler on antisymmetrizer determinant formulas

Primary source

Additional references

Progress summary

Solutions 0