PreprintCC BY 4.0arXiv
Combinatorial formulas for the multivariate Markov-Krein transform
Abstract
In this work, we study the Markov--Krein correspondence in both the univariate and multivariate settings. Our main result provides an explicit moment--moment formula expressing the multivariate moments of the inverse Markov--Krein transform in terms of the multivariate moments of the Markov-Krein transform via cyclic interval partitions. We also derive moment--cumulant relations involving classical, Boolean and free cumulants.
Related
- Stability of the Markov-Krein Transform Under Classical Convolutions
- Combinatorial Goussarov-Polyak-Viro Formulas for the Linking Number and Low Degree Coefficients of the Conway Polynomial
- Combinatorial identities derived from explicit formulas of Gauss hypergeometric functions
- GNS-like representations of a quasi *-algebra in Krein spaces
- Compressions of Linear Relations in Krein Spaces
BibTeX
@misc{zazuetaobeso2026combinatorial,
title = {{Combinatorial formulas for the multivariate Markov-Krein transform}},
author = {Julian Zazueta-Obeso},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30155},
eprint = {2610.30155},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30155},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Combinatorial formulas for the multivariate Markov-Krein transform
AU - Julian Zazueta-Obeso
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.30155
UR - https://arxiv.org/abs/2610.30155
AB - In this work, we study the Markov--Krein correspondence in both the univariate and multivariate settings. Our main result provides an explicit moment--moment formula expressing the multivariate moments of the inverse Markov--Krein transform in terms of the multivariate moments of the Markov-Krein transform via cyclic interval partitions. We also derive moment--cumulant relations involving classical, Boolean and free cumulants.
ER -