Noncommutative algebra, multiple harmonic sums and applications in discrete probability

DOI10.1016/j.jsc.2008.04.008zbMath1179.11030OpenAlexW2015685619MaRDI QIDQ1025389

Christian Costermans, Vincel Hoang Ngoc Minh

Publication date: 18 June 2009

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jsc.2008.04.008

zbMATH Keywords

polylogarithmasymptotic analysismultiple zeta valuediscrete probabilityharmonic sum

Mathematics Subject Classification ID

Permutations, words, matrices (05A05) (zeta (s)) and (L(s, chi)) (11M06) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Combinatorial probability (60C05) General nonassociative rings (17A99) Polylogarithms and relations with (K)-theory (11G55) Higher logarithm functions (33B30) Multiple Dirichlet series and zeta functions and multizeta values (11M32)

Related Items (9)

Structure of polyzetas and explicit representation on transcendence bases of shuffle and stuffle algebras ⋮ Harmonic sums and polylogarithms at non-positive multi-indices ⋮ Towards a theory of domains for harmonic functions and its symbolic counterpart ⋮ Natural endomorphisms of quasi-shuffle Hopf algebras ⋮ Combinatorial properties and effective analytic continuation of Hurwitz polyzetas and their analogous ⋮ (Pure) transcendence bases in \(\varphi\)-deformed shuffle bialgebras ⋮ Structure of polyzetas and Lyndon words ⋮ On the solutions of the universal differential equation with three regular singularities (on solutions of \(KZ_3)\) ⋮ Kleene stars of the plane, polylogarithms and symmetries

Cites Work

• A natural ring basis for the shuffle algebra and an application to group schemes
• On the variance of the number of maxima in random vectors and its applications
• Combinatorial variations on multidimensional quadtrees
• The algebra of multiple harmonic series
• Shuffle algebra and polylogarithms
• On the distribution of the arity of the root of a \(d\)-dimensional quadtree
• Duality between quasi-symmetric functions and the Solomon descent algebra
• Quasi-shuffle products
• On the Distribution of the Number of Admissible Points in a Vector Random Sample
• Algebraic Aspects of Multiple Zeta Values
• Structure and asymptotic expansion of multiple harmonic sums
• Maxima in hypercubes
• The hyperharmonic numbers and the phratry of the coupon collector
• From the algebras of Riemann polyzetas to the algebra of Hurwitz polyzetas
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