Results 21 to 30 of about 3,007,169 (162)
Noncommutative Symmetrical Functions
Advances in Mathematics, 1995 This paper presents a noncommutative theory of symmetric functions, based on the notion of quasi-determinant. We begin with a formal theory, corresponding to the case of symmetric functions in an infinite number of independent variables. This allows us to endow the resulting algebra with a Hopf structure, which leads to a new method for computing in ...
Gelfand, Israel M. +5 more
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Noncommutative Symmetric Functions II: Transformations of Alphabets [PDF]
International Journal of Algebra and Computation, 1997 Noncommutative analogues of classical operations on symmetric functions are investigated, and applied to the description of idempotents and nilpotents in descent algebras. It is shown that any sequence of Lie idempotents (one in each descent algebra) gives rise to a complete set of indecomposable orthogonal idempotents of each descent algebra, and ...
Krob, Daniel +2 more
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A commutative noncommutative fractal geometry [PDF]
, 2010 In this thesis examples of spectral triples, which represent fractal sets, are examined and new insights into their noncommutative geometries are obtained.
Samuel, Tony; id_orcid +6 more
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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, ${\
Mahir Bilen Can, Bruce E. Sagan
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Chromatic symmetric functions in noncommuting variables revisited [PDF]
Advances in Applied Mathematics, 2020 23 pages, final version to appear Adv.
Samantha Dahlberg +1 more
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Advances in Difference Equations, 2020 Quantum calculus (the calculus without limit) appeared for the first time in fluid mechanics, noncommutative geometry and combinatorics studies. Recently, it has been included into the field of geometric function theory to extend differential operators ...
Rabha W. Ibrahim +2 more
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Unital versions of the higher order peak algebras [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 We construct unital extensions of the higher order peak algebras defined by Krob and the third author in [Ann. Comb. 9 (2005), 411―430], and show that they can be obtained as homomorphic images of certain subalgebras of the Mantaci-Reutenauer algebras of
Marcelo Aguiar +2 more
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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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Card-Shuffling via Convolutions of Projections on Combinatorial Hopf Algebras [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 Recently, Diaconis, Ram and I created Markov chains out of the coproduct-then-product operator on combinatorial Hopf algebras. These chains model the breaking and recombining of combinatorial objects.
C. Y. Amy Pang
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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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