Salvato in:
| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2404.15119 |
| Tags: |
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Sommario:
- We introduce the theory of normal ordered grammars, which gives a natural generalization of the normal ordering problem. To illustrate the main idea, we explore normal ordered grammars associated with the Eulerian polynomials and the second-order Eulerian polynomials. In particular, we present a normal ordered grammatical interpretation for the (cdes,cyc) (p,q)-Eulerian polynomials, where cdes and cyc are the cycle descent and cycle statistics, respectively. The exponential generating function for a family of polynomials, generated by a normal ordered grammar associated with the second-order Eulerian polynomials, reveals an interesting feature: its expression involves the generating function for Catalan numbers as its exponent. In the final part, we discuss some normal ordered grammars related to the type B Eulerian polynomials. A normal ordered grammatical interpretation of the up-down run polynomial is also established.