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A valley version of the Delta square conjecture

par Iraci, Alessandro ;Vanden Wyngaerd, Anna
Référence Annals of combinatorics
Publication A Paraître, 2021-04-01

Article révisé par les pairs

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Résumé :

Inspired by [Qiu, Wilson 2019] and [D'Adderio, Iraci, Vanden Wyngaerd 2019 - Delta Square], we formulate a generalised Delta square conjecture (valley version). Furthermore, we use similar techniques as in [Haglund, Sergel 2019] to obtain a schedule formula for the combinatorics of our conjecture. We then use this formula to prove that the (generalised) valley version of the Delta conjecture implies our (generalised) valley version of the Delta square conjecture. This implication broadens the argument in [Sergel 2016], relying on the formulation of the touching version in terms of the Θf operators introduced in [D'Adderio, Iraci, Vanden Wyngaerd 2019 - Theta Operators].