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unknown title
, 2013
"... Dual bases for non commutative symmetric and quasisymmetric functions via monoidal factorization ..."
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Dual bases for non commutative symmetric and quasisymmetric functions via monoidal factorization
Quasisymmetric functions and the KP hierarchy
, 2009
"... Quasisymmetric functions show up in an approach to solve the KadomtsevPetviashvili (KP) hierarchy. This moreover features a new nonassociative product of quasisymmetric functions that satisfies simple relations with the ordinary product and the outer coproduct. In particular, supplied with this n ..."
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Quasisymmetric functions show up in an approach to solve the KadomtsevPetviashvili (KP) hierarchy. This moreover features a new nonassociative product of quasisymmetric functions that satisfies simple relations with the ordinary product and the outer coproduct. In particular, supplied
Super quasisymmetric functions via Young diagrams
"... Abstract. We consider the multivariate generating series FP of Ppartitions in infinitely many variables x1, x2,.... For some family of ranked posets P, it is natural to consider an analog NP with two infinite alphabets. When we collapse these two alphabets, we trivially recover FP. Our main result ..."
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Cited by 1 (1 self)
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principal est la réciproque de cela: nous montrons qu’il existe une opération retournant NP a ̀ partir de FP. Nous donnons aussi un analogue noncommutatif de cette opération. Nous obtenons ainsi une nouvelle base de WQSym, base qui relève une base de K. Luoto et dont les coefficients de structure sont
Catalan Paths and QuasiSymmetric Functions
 Proc. Amer. Math. Soc
"... Abstract. We investigate the quotient ring R of the ring of formal power series Q[[x1, x2,...]] over the closure of the ideal generated by nonconstant quasisymmetric functions. We show that a Hilbert basis of the quotient is naturally indexed by Catalan paths (infinite Dyck paths). We also give a f ..."
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Cited by 9 (6 self)
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filtration of ideals related to Catalan paths from (0, 0) and above the line y = x−k. We investigate as well the quotient ring Rn of polynomial ring in n variables over the ideal generated by nonconstant quasisymmetric polynomials. We show that the dimension of Rn is bounded above by the nth Catalan number
Symmetric and QuasiSymmetric Functions Associated to Polymatroids
, 2008
"... To every subspace arrangement X we will associate symmetric functions P[X] and H[X]. These symmetric functions encode the Hilbert series and the minimal projective resolution of the product ideal associated to the subspace arrangement. They can be defined for discrete polymatroids as well. The invar ..."
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Cited by 9 (1 self)
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. The invariant H[X] specializes to the Tutte polynomial T [X]. Billera, Jia and Reiner recently introduced a quasisymmetric function F[X] (for matroids) which behaves valuatively with respect to matroid base polytope decompositions. We will define a quasisymmetric function G[X] for polymatroids which has
Structure of the peak Hopf algebra of quasisymmetric functions
, 2002
"... Abstract. We analyze the structure of Stembridge’s peak algebra, showing it to be a free commutative algebra (specifically a shuffle algebra) over Q, a cofree graded coalgebra, and a free module over Schur’s Qfunction algebra. Our analysis builds on combinatorial properties of a new monomiallik ..."
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Cited by 5 (0 self)
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Abstract. We analyze the structure of Stembridge’s peak algebra, showing it to be a free commutative algebra (specifically a shuffle algebra) over Q, a cofree graded coalgebra, and a free module over Schur’s Qfunction algebra. Our analysis builds on combinatorial properties of a new monomial
Noncommutative Symmetric Functions VII: Free QuasiSymmetric Functions Revisited
, 2008
"... We prove a Cauchy identity for free quasisymmetric functions and apply it to the study of various bases. A free Weyl formula and a generalization of the splitting formula are also discussed. ..."
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Cited by 14 (10 self)
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We prove a Cauchy identity for free quasisymmetric functions and apply it to the study of various bases. A free Weyl formula and a generalization of the splitting formula are also discussed.
Logical foundations of objectoriented and framebased languages
 JOURNAL OF THE ACM
, 1995
"... We propose a novel formalism, called Frame Logic (abbr., Flogic), that accounts in a clean and declarative fashion for most of the structural aspects of objectoriented and framebased languages. These features include object identity, complex objects, inheritance, polymorphic types, query methods, ..."
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Cited by 880 (64 self)
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We propose a novel formalism, called Frame Logic (abbr., Flogic), that accounts in a clean and declarative fashion for most of the structural aspects of objectoriented and framebased languages. These features include object identity, complex objects, inheritance, polymorphic types, query methods
Bidendriform bialgebras, trees, and free quasisymmetric functions
"... ABSTRACT: we introduce bidendriform bialgebras, which are bialgebras such that both product and coproduct can be split into two parts satisfying good compatibilities. For example, the MalvenutoReutenauer Hopf algebra and the noncommutative ConnesKreimer Hopf algebras of planar decorated rooted tr ..."
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Cited by 24 (1 self)
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ABSTRACT: we introduce bidendriform bialgebras, which are bialgebras such that both product and coproduct can be split into two parts satisfying good compatibilities. For example, the MalvenutoReutenauer Hopf algebra and the noncommutative ConnesKreimer Hopf algebras of planar decorated rooted
Dual polyhedra and mirror symmetry for Calabi–Yau hypersurfaces in toric varieties
 J. Alg. Geom
, 1994
"... We consider families F(∆) consisting of complex (n − 1)dimensional projective algebraic compactifications of ∆regular affine hypersurfaces Zf defined by Laurent polynomials f with a fixed ndimensional Newton polyhedron ∆ in ndimensional algebraic torus T = (C ∗ ) n. If the family F(∆) defined by ..."
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Cited by 467 (20 self)
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by a Newton polyhedron ∆ consists of (n − 1)dimensional CalabiYau varieties then the dual, or polar, polyhedron ∆ ∗ in the dual space defines another family F( ∆ ∗ ) of CalabiYau varieties, so that we obtain the remarkable duality between two different families of CalabiYau varieties. It is shown
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