Explicit Expressions for the First 20 Moments of the Area Under Dyck and Motzkin Paths

Fuente: arXiv
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Autori principali: Bu, AJ, Ekhad, Shalosh B., Zeilberger, Doron
Natura: Preprint
Pubblicazione: 2024
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author Bu, AJ
Ekhad, Shalosh B.
Zeilberger, Doron
author_facet Bu, AJ
Ekhad, Shalosh B.
Zeilberger, Doron
contents Starting from AJ Bu's recent article that computed explicit expressions for the GENERATING functions of sums of powers of areas under Dyck and Motzkin paths, we deduce from them explicit expressions for the actual sequences. This enables taking the limits of the scaled moments and confirming, in an entirely elementary way, that they tend to those of the area under Brownian Excursion (up to any specified moment).
format Preprint
id arxiv_https___arxiv_org_abs_2405_03079
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Explicit Expressions for the First 20 Moments of the Area Under Dyck and Motzkin Paths
Bu, AJ
Ekhad, Shalosh B.
Zeilberger, Doron
Combinatorics
Starting from AJ Bu's recent article that computed explicit expressions for the GENERATING functions of sums of powers of areas under Dyck and Motzkin paths, we deduce from them explicit expressions for the actual sequences. This enables taking the limits of the scaled moments and confirming, in an entirely elementary way, that they tend to those of the area under Brownian Excursion (up to any specified moment).
title Explicit Expressions for the First 20 Moments of the Area Under Dyck and Motzkin Paths
topic Combinatorics
url https://arxiv.org/abs/2405.03079