We also prove some that, for a large class of patterns, the inverse of the exponential generating function counting occurrences is an entire function, but we conjecture that it is not D-finite in general.
On démontre aussi que, pour une grande classe de motifs, l'inverse de la série génératrice exponentielle qui compte occurrences est une fonction entière, mais on conjecture qu'elle n'est pas D-finie en général.
The exponential generating function of the ordered Bell numbers is
Using Shareshian and Wachs' exponential generating function of these Eulerian polynomials, Chung and Graham proved two symmetrical q-Eulerian identities and asked for bijective proofs.
En utilisant la fonction génératrice de ces polynômes Eulériens due à Shareshien et Wachs, Chung et Graham ont démontré deux identités symétriques q-Eulériennes et demandé des preuves bijectives.
In combinatorial mathematics, the exponential formula (called the polymer expansion in physics) states that the exponential generating function for structures on finite sets is the exponential of the exponential generating function for connected structures.
En combinatoire, la formule exponentielle (appelée expansion du polymère en physique) établit que la fonction génératrice exponentielle pour les structures sur des ensembles finis est l'exponentielle de la fonction génératrice exponentielle pour les structures connectées.
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Synonyms and analogies of "exponential generating function" in English