منابع مشابه
Plethystic Algebra
The notion of a Z-algebra has a non-linear analogue, whose purpose it is to control operations on commutative rings rather than linear operations on abelian groups. These plethories can also be considered non-linear generalizations of cocommutative bialgebras. We establish a number of categorytheoretic facts about plethories and their actions, including a Tannaka–Kreinstyle reconstruction theor...
متن کاملPlethystic F Ormulas For
This work is concerned with the Macdonald q;t-analogue of the Kostka matrix. This matrix relates the two parameter Macdonald basis fP x; q;tg to the modiied Schur basis fS X1 , tg. The entries in this matrix, which h a v e come to be denoted by K ; q;t, h a v e been conjectured by Macdonald to be polynomials in q;t with positive i n tegral coeecients. Our main main result here is an algorithm f...
متن کاملPlethystic algebras and vector symmetric functions.
An isomorphism is established between the plethystic Hopf algebra Pleth(Super[L]) and the algebra of vector symmetric functions. The Hall inner product of symmetric function theory is extended to the Hopf algebra Pleth(Super[L]).
متن کاملA Combinatorial Proof of a Plethystic
The purpose of this note is to give a combinatorial proof of a plethystic generalization of the Murnaghan–Nakayama rule, first stated in [1]. The key step in the proof uses a sign-reversing pairing on sequences of bead moves on James’ abacus (see [3, page 78]), inspired by the theme of [4] ‘when beads bump, objects cancel’. The only prerequisites are the Murnaghan– Nakayama rule and basic facts...
متن کاملSome Plethystic Identities And Kostka-Foulkes Polynomials
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) → Λ n Q(q,t) be the Garsia-Bergeron operator. By studying recursions, Garsia and Haglund show that the coefficient of the elementary symmetric function en(X) in the image ∇(En,k(X))...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2005
ISSN: 0001-8708
DOI: 10.1016/j.aim.2004.06.006