On the Schur positivity of Δ_e2 e_n[X]

2017/10/09 by Qiu, Dun, Remmel, Jeffrey B., Sergel, Emily +1
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1710.03340

Abstract

Let ℕ denote the set of non-negative integers. Haglund, Wilson, and the second author have conjectured that the coefficient of any Schur function s_λ[X] in Δ_ek e_n[X] is a polynomial in ℕ[q,t]. We present four proofs of a stronger statement in the case k=2; We show that the coefficient of any Schur function s_λ[X] in Δ_e2 e_n[X] has a positive expansion in terms of q,t-analogs.

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