Results 11 to 20 of about 131 (118)
The # product in combinatorial Hopf algebras [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 We show that the # product of binary trees introduced by Aval and Viennot (2008) is in fact defined at the level of the free associative algebra, and can be extended to most of the classical combinatorial Hopf algebras.
Jean-Christophe Aval +2 more
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From Hurwitz numbers to Feynman diagrams: Counting rooted trees in log gravity
Nuclear Physics B, 2023 We show that the partition function of the logarithmic sector of critical topologically massive gravity which represents a series expansion of composition of functions, can be expressed as a sum over rooted trees.
Yannick Mvondo-She
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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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Supercharacters, symmetric functions in noncommuting variables (extended abstract) [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 We identify two seemingly disparate structures: supercharacters, a useful way of doing Fourier analysis on the group of unipotent uppertriangular matrices with coefficients in a finite field, and the ring of symmetric functions in noncommuting variables.
Marcelo Aguiar +27 more
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A combinatorial non-commutative Hopf algebra of graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 Combinatorics A non-commutative, planar, Hopf algebra of planar rooted trees was defined independently by one of the authors in Foissy (2002) and by R. Holtkamp in Holtkamp (2003). In this paper we propose such a non-commutative Hopf algebra for graphs. In order to define a non-commutative product we use a quantum field theoretical (QFT) idea,
Duchamp, Gerard +4 more
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Invariant and coinvariant spaces for the algebra of symmetric polynomials in non-commuting variables [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 We analyze the structure of the algebra $\mathbb{K}\langle \mathbf{x}\rangle^{\mathfrak{S}_n}$ of symmetric polynomials in non-commuting variables in so far as it relates to $\mathbb{K}[\mathbf{x}]^{\mathfrak{S}_n}$, its commutative counterpart.
François Bergeron, Aaron Lauve
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The Cambrian Hopf Algebra [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 Cambrian trees are oriented and labeled trees which fulfill local conditions around each node generalizing the conditions for classical binary search trees.
G. Chatel, V. Pilaud
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Combinatorial Hopf Algebras and K-Homology of Grassmanians [PDF]
International Mathematics Research Notices, 2010 Motivated by work of Buch on set-valued tableaux in relation to the K-theory of the Grassmannian, we study six combinatorial Hopf algebras. These Hopf algebras can be thought of as K-theoretic analogues of the by now classical ``square'' of Hopf algebras consisting of symmetric functions, quasisymmetric functions, noncommutative symmetric functions and
Lam, Thomas, Pylyavskyy, Pavlo
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A Hopf-power Markov chain on compositions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 In a recent paper, Diaconis, Ram and I constructed Markov chains using the coproduct-then-product map of a combinatorial Hopf algebra. We presented an algorithm for diagonalising a large class of these "Hopf-power chains", including the Gilbert-Shannon ...
C.Y. Amy Pang
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Coloring Rings in Species [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 We present a generalization of the chromatic polynomial, and chromatic symmetric function, arising in the study of combinatorial species. These invariants are defined for modules over lattice rings in species.
Jacob White
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