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We introduce the Macdonald piece polynomial I, , ₊X;q, t, which is a vast generalization of the Macdonald intersection polynomial in the science fiction conjecture by Bergeron and Garsia. We demonstrate a remarkable connection between I, , ₊, s_, and the Loehr--Warrington formula LW_, thereby obtaining the Loehr--Warrington conjecture as a corollary. To connect I, , ₊ and s_, we employ the plethystic formula for the Macdonald polynomials of Garsia--Haiman--Tesler, and to connect I, , ₊ and LW_, we use our new findings on the combinatorics of P-tableaux together with the column exchange rule. We also present an extension of the science fiction conjecture and the Macdonald positivity by exploiting I, , ₊.
Kim et al. (Mon,) studied this question.