A Valley Version of the Delta Square Conjecture

Inspired by Qiu and Wilson (J Combin Theory Ser A 175:105271, 2020) and D’Adderio et al. (Eur J Combin 81:58–83, 2019), we formulate a generalised Delta square conjecture (valley version). Furthermore, we use similar techniques as in Haglund and Sergel (Schedules and the delta conjecture, arXiv:1908.04732, 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 et al. (Adv Math 107447, 2020).