PreprintCC BY 4.0arXiv
Alternating Sums in Compositions
Abstract
Motivated by the recent asymptotic formula for the moment of the alternating sum of parts in partitions by Craig and Li, we study the moment of the alternating sum of parts in compositions. We establish closed formulas for this moment using techniques involving generating functions, matrix diagonalization, Krawtchouk polynomials, differential equations, and Faà di Bruno's formula. Our result is connected with some known integer sequences in the OEIS and admits a combinatorial interpretation by coin flipping.
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BibTeX
@misc{gao2026alternating,
title = {{Alternating Sums in Compositions}},
author = {Runde Gao and Jia Huang},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01919},
eprint = {2611.01919},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01919},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Alternating Sums in Compositions
AU - Runde Gao
AU - Jia Huang
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01919
UR - https://arxiv.org/abs/2611.01919
AB - Motivated by the recent asymptotic formula for the moment of the alternating sum of parts in partitions by Craig and Li, we study the moment of the alternating sum of parts in compositions. We establish closed formulas for this moment using techniques involving generating functions, matrix diagonalization, Krawtchouk polynomials, differential equations, and Faà di Bruno's formula. Our result is connected with some known integer sequences in the OEIS and admits a combinatorial interpretation by coin flipping.
ER -