Some Plethystic Identites and Kostka-foulkes Polynomials

  • Published 2012
plays an important role in the Garsia-Haglund proof of the q, t-Catalan conjecture, [2]. Let ΛQ(q,t) be the space of symmetric functions of degree n, over the field of rational functions Q(q, t), and let ∇ : ΛQ(q,t) → ΛQ(q,t) be the Garsia-Bergeron operator. By studying recursions, Garsia and Haglund show that the coefficient of the elementary symmetric… (More)