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On how many Fibonacci words is the Plancherel measure concentrated
Abstract
On the set 𝕐𝔽n of words in $1$ and $2$ with digit sum n, we consider the probability distribution μP, corresponding to the Plancherel measure on paths in the Young--Fibonacci graph. We study the asymptotics as n grows of the entropy of the distribution μP and of the minimum number of words on which μP is almost entirely concentrated.
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BibTeX
@misc{evtushevsky2026many,
title = {{On how many Fibonacci words is the Plancherel measure concentrated}},
author = {Vsevolod Evtushevsky},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06585},
eprint = {2610.06585},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06585},
}
RIS
TY - UNPB
TI - On how many Fibonacci words is the Plancherel measure concentrated
AU - Vsevolod Evtushevsky
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06585
UR - https://arxiv.org/abs/2610.06585
AB - On the set 𝕐𝔽_n of words in $1$ and $2$ with digit sum n, we consider the probability distribution μ_P, corresponding to the Plancherel measure on paths in the Young--Fibonacci graph. We study the asymptotics as n grows of the entropy of the distribution μ_P and of the minimum number of words on which μ_P is almost entirely concentrated.
ER -