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                  <biblScope unit="volume">DMTCS Proceedings vol. AO, 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011)</biblScope>
                  <biblScope unit="pp">3-14</biblScope>
                  <date type="datePub">2011-01-01</date>
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              <idno type="doi">10.46298/dmtcs.2967</idno>
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                <term xml:lang="en"> Hopf algebras</term>
                <term xml:lang="en"> symmetric functions in non-commuting variables</term>
                <term xml:lang="en"> set partitions</term>
                <term xml:lang="en">supercharacters</term>
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              <classCode scheme="halDomain" n="info">Computer Science [cs]</classCode>
              <classCode scheme="halDomain" n="math">Mathematics [math]</classCode>
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              <p>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. Each is a Hopf algebra and the two are isomorphic as such. This allows developments in each to be transferred. The identification suggests a rich class of examples for the emerging field of combinatorial Hopf algebras.</p>
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              <p>Nous montrons que deux structures en apparence bien différentes peuvent être identifiées: les super-caractères, qui sont un outil commode pour faire de l'analyse de Fourier sur le groupe des matrices unipotentes triangulaires supérieures à coefficients dans un corps fini, et l'anneau des fonctions symétriques en variables non-commutatives. Ces deux structures sont des algèbres de Hopf isomorphes. Cette identification permet de traduire dans une structure les dévelopements conçus pour l'autre, et suggère de nombreux exemples dans le domaine nouveau des algèbres de Hopf combinatoires.</p>
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