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# Noncommutative Symmetric Bessel Functions

Published:2008-09-01
Printed: Sep 2008
• Jean-Christophe Novelli
• Jean-Yves Thibon
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## Abstract

The consideration of tensor products of $0$-Hecke algebra modules leads to natural analogs of the Bessel $J$-functions in the algebra of noncommutative symmetric functions. This provides a simple explanation of various combinatorial properties of Bessel functions.
 MSC Classifications: 05E05 - Symmetric functions and generalizations 16W30 - Coalgebras, bialgebras, Hopf algebras (See also 16S40, 57T05); rings, modules, etc. on which these act05A15 - Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx]