Results 31 to 40 of about 20,221 (160)
A Chromatic Symmetric Function in Noncommuting Variables [PDF]
Journal of Algebraic Combinatorics, 2001 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gebhard, David D., Sagan, Bruce E.
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Colored Trees and Noncommutative Symmetric Functions [PDF]
The Electronic Journal of Combinatorics, 2010 Let ${\cal CRF}_S$ denote the category of $S$-colored rooted forests, and H$_{{\cal CRF}_S}$ denote its Ringel-Hall algebra as introduced by Kremnizer and Szczesny. We construct a homomorphism from a $K^+_0({\cal CRF}_S)$–graded version of the Hopf algebra of noncommutative symmetric functions to H$_{{\cal CRF}_S}$. Dualizing, we obtain a homomorphism
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Noncommutative symmetric functions and Lagrange inversion
Advances in Applied Mathematics, 2008 22 pages, 8 figures ...
Novelli, Jean-Christophe +1 more
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The Polarization Theorem and Polynomial Identities for Matrix Functions
Известия Иркутского государственного университета: Серия "Математика", 2017 In this article the simple combinatorial proof of the known polarization theorem (about the restoration of a polyadditive symmetric function over its values on a diagonal) is given.
G.P. Egorychev
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Symmetric functions of two noncommuting variables [PDF]
Journal of Functional Analysis, 2014 We prove a noncommutative analogue of the fact that every symmetric analytic function of $(z,w)$ in the bidisc $\D^2$ can be expressed as an analytic function of the variables $z+w$ and $zw$. We construct an analytic nc-map $S$ from the biball to an infinite-dimensional nc-domain $ $ with the property that, for every bounded symmetric function $\ph ...
Agler J, Young NJ
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Hasse-Schmidt Derivations and the Hopf Algebra of Non-Commutative Symmetric Functions
Axioms, 2012 Let NSymm be the Hopf algebra of non-commutative symmetric functions (in an infinity of indeterminates): . It is shown that an associative algebra A with a Hasse-Schmidt derivation ) on it is exactly the same as an NSymm module algebra. The primitives of
Michiel Hazewinkel
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NONCOMMUTATIVE SYMMETRIC FUNCTIONS AND THE INVERSION PROBLEM [PDF]
International Journal of Algebra and Computation, 2008 Let K be any unital commutative ℚ-algebra and z = (z1, z2, …, zn) commutative or noncommutative variables. Let t be a formal central parameter and K[[t]]〈〈z〉〉 the formal power series algebra of z over K[[t]]. In [29], for each automorphism Ft(z) = z - Ht(z) of K[[t]]〈〈z〉〉 with Ht=0(z) = 0 and o(H(z)) ≥ 1, a [Formula: see text] (noncommutative symmetric)
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Partitions, Rooks, and Symmetric Functions in Noncommuting Variables [PDF]
The Electronic Journal of Combinatorics, 2011 Let $\Pi_n$ denote the set of all set partitions of $\{1,2,\ldots,n\}$. We consider two subsets of $\Pi_n$, one connected to rook theory and one associated with symmetric functions in noncommuting variables. Let ${\cal E}_n\subseteq\Pi_n$ be the subset of all partitions corresponding to an extendable rook (placement) on the upper-triangular board, ${\
Can, Mahir Bilen, Sagan, Bruce E.
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Determinants as Combinatorial Summation Formulas over an Algebra with a Unique $n$-ary Operation
Известия Иркутского государственного университета: Серия "Математика", 2018 Since the late 1980s the author has published a number of results on matrix functions, which were obtained using the generating functions, mixed discriminants (mixed volumes in $\mathbb R^n$), and the well-known polarization theorem (the most general ...
G.P. Egorychev
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Quasi-symmetric functions as polynomial functions on Young diagrams [PDF]
, 2014 We determine the most general form of a smooth function on Young diagrams, that is, a polynomial in the interlacing or multirectangular coordinates whose value depends only on the shape of the diagram.
Aval, Jean-Christophe +3 more
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