An Explicit Schur Expansion for Big-Descent Quasisymmetric Functions of 123-Avoiding Permutations

We study the quasisymmetric function recording positions of big descents in 123-avoiding permutations. Its monomial coefficient factors as a Catalan number times the product of the composition parts, establishing symmetry. A constant-term specialization yields an explicit nonnegative Schur expansion in every degree. This provides the length-three case of the increasing-pattern conjecture of Elizalde, Rivera, and Zhuang (2026). The manuscript is a preprint that has not undergone human peer review. Novelty is inconclusive. AI-assisted review and reproducibility checks are documented with their limitations.