Results 31 to 40 of about 28,962 (144)
The dynamics of non-perturbative phases via Banach bundles
Nuclear Physics B, 2021 Strongly coupled Dyson–Schwinger equations generate infinite power series of running coupling constants together with Feynman diagrams with increasing loop orders as coefficients. Theory of graphons for sparse graphs can address a new useful approach for
Ali Shojaei-Fard
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Partial categorification of Hopf algebras and representation theory of towers of \mathcalJ-trivial monoids [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 This paper considers the representation theory of towers of algebras of $\mathcal{J} -trivial$ monoids. Using a very general lemma on induction, we derive a combinatorial description of the algebra and coalgebra structure on the Grothendieck rings $G_0 ...
Aladin Virmaux
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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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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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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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Peak algebras in combinatorial Hopf algebras
, 2021 The peak algebra is originally introduced by Stembridge using enriched $P$-partitions. Using the character theory by Aguiar-Bergeron-Sottile, the peak algebra is also the image of $ $, the universal morphism between certain combinatorial Hopf algebras. We extend the notion of peak algebras and theta maps to shuffle, tensor, and symmetric algebras.
Aliniaeifard, Farid, Li, Shu Xiao
openaire +2 more sources
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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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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From left modules to algebras over an operad: application to combinatorial Hopf algebras [PDF]
, 2009 The purpose of this paper is two fold: we study the behaviour of the forgetful functor from S-modules to graded vector spaces in the context of algebras over an operad and derive from this theory the construction of combinatorial Hopf algebras.
Livernet, Muriel
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Dendriform structures for restriction-deletion and restriction-contraction matroid Hopf algebras [PDF]
Discrete Mathematics & Theoretical Computer Science, 2016 We endow the set of isomorphism classes of matroids with a new Hopf algebra structure, in which the coproduct is implemented via the combinatorial operations of restriction and deletion.
Nguyen Hoang-Nghia +2 more
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