Asymptotic normality for the count of distinct entries in uniformly random inversion sequences avoiding 010 and 0211

Gökhan Yıldırım

doi:10.26650/ijmath.2025.00028

Asymptotic normality for the count of distinct entries in uniformly random inversion sequences avoiding 010 and 0211

Abstract

We study the class of inversion sequences of length 𝑛 that avoid the patterns 010 and 0211, denoted 𝐼𝑛 (010, 0211). We construct an explicit bijection between this class and the set of partitions of [𝑛] := {1, 2, 3, · · · , 𝑛}. This correspondence allows us to interpret natural statistics on 𝐼𝑛 (010, 0211) in terms of classical statistics on set partitions. In particular, we show that the number of distinct entries in an inversion sequence from 𝐼𝑛 (010, 0211) corresponds to the number of blocks in the associated partition of [𝑛]. As a consequence, the distribution of this statistic is governed by Stirling numbers of the second kind, which in turn leads to a central limit theorem for the number of distinct entries in a random element of 𝐼𝑛 (010, 0211).

Keywords

References

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Details

Primary Language

English

Subjects

Pure Mathematics (Other)

Journal Section

Research Article

Authors

Gökhan Yıldırım ^*
0000-0003-4399-7843
Türkiye

Publication Date

December 16, 2025

Submission Date

September 1, 2025

Acceptance Date

December 11, 2025

Published in Issue

Year 2025 Volume: 3 Number: 2

DOI

https://doi.org/10.26650/ijmath.2025.00028

IZ

https://izlik.org/JA38TG69YC

Cite

RIS / Bibtex

APA

Yıldırım, G. (2025). Asymptotic normality for the count of distinct entries in uniformly random inversion sequences avoiding 010 and 0211. Istanbul Journal of Mathematics, 3(2), 61-65. https://doi.org/10.26650/ijmath.2025.00028

AMA

1.Yıldırım G. Asymptotic normality for the count of distinct entries in uniformly random inversion sequences avoiding 010 and 0211. Istanbul Journal of Mathematics. 2025;3(2):61-65. doi:10.26650/ijmath.2025.00028

Chicago

Yıldırım, Gökhan. 2025. “Asymptotic Normality for the Count of Distinct Entries in Uniformly Random Inversion Sequences Avoiding 010 and 0211”. Istanbul Journal of Mathematics 3 (2): 61-65. https://doi.org/10.26650/ijmath.2025.00028.

EndNote

Yıldırım G (December 1, 2025) Asymptotic normality for the count of distinct entries in uniformly random inversion sequences avoiding 010 and 0211. Istanbul Journal of Mathematics 3 2 61–65.

IEEE

[1]G. Yıldırım, “Asymptotic normality for the count of distinct entries in uniformly random inversion sequences avoiding 010 and 0211”, Istanbul Journal of Mathematics, vol. 3, no. 2, pp. 61–65, Dec. 2025, doi: 10.26650/ijmath.2025.00028.

ISNAD

Yıldırım, Gökhan. “Asymptotic Normality for the Count of Distinct Entries in Uniformly Random Inversion Sequences Avoiding 010 and 0211”. Istanbul Journal of Mathematics 3/2 (December 1, 2025): 61-65. https://doi.org/10.26650/ijmath.2025.00028.

JAMA

1.Yıldırım G. Asymptotic normality for the count of distinct entries in uniformly random inversion sequences avoiding 010 and 0211. Istanbul Journal of Mathematics. 2025;3:61–65.

MLA

Yıldırım, Gökhan. “Asymptotic Normality for the Count of Distinct Entries in Uniformly Random Inversion Sequences Avoiding 010 and 0211”. Istanbul Journal of Mathematics, vol. 3, no. 2, Dec. 2025, pp. 61-65, doi:10.26650/ijmath.2025.00028.

Vancouver

1.Gökhan Yıldırım. Asymptotic normality for the count of distinct entries in uniformly random inversion sequences avoiding 010 and 0211. Istanbul Journal of Mathematics. 2025 Dec. 1;3(2):61-5. doi:10.26650/ijmath.2025.00028