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While equality of skew Schur functions is well understood, the problem ofdetermining when two skew Schur $Q$ functions are equal is still largely open.It has been studied in the case of ribbon shapes in 2008 by Barekat and vanWilligenburg, and this paper approaches the problem for near-ribbon shapes,formed by adding one box to a ribbon skew shape. We particularly considerfrayed ribbons, that is, the near-ribbons whose shifted skew shape is not anordinary skew shape. We conjecture, with evidence, that all Schur $Q$ functionsof frayed ribbon shape are distinct up to antipodal reflection. We prove thisconjecture for several infinite families of frayed ribbons, using a newapproach via the "lattice walks" version of the shifted Littlewood-Richardsonrule discovered in 2018 by Gillespie, Levinson, and Purbhoo.

Inequality of a class of near-ribbon skew Schur Q-functions