Geodesic
The number of distinct adjacent pairs in geometrically distributed words: a probabilistic and combinatorial analysis
Discrete mathematics & theoretical computer science, Tome 25 (2023-2024) no. 2.

Voir la notice de l'article provenant de la source Episciences

The analysis of strings of $n$ random variables with geometric distribution has recently attracted renewed interest: Archibald et al. consider the number of distinct adjacent pairs in geometrically distributed words. They obtain the asymptotic ($n\rightarrow\infty$) mean of this number in the cases of different and identical pairs. In this paper we are interested in all asymptotic moments in the identical case, in the asymptotic variance in the different case and in the asymptotic distribution in both cases. We use two approaches: the first one, the probabilistic approach, leads to variances in both cases and to some conjectures on all moments in the identical case and on the distribution in both cases. The second approach, the combinatorial one, relies on multivariate pattern matching techniques, yielding exact formulas for first and second moments. We use such tools as Mellin transforms, Analytic Combinatorics, Markov Chains.
DOI : 10.46298/dmtcs.9293
Classification : 05A15, 68R15 
@article{DMTCS_2024_25_2_a8,
     author = {Louchard, Guy and Schachinger, Werner and Ward, Mark Daniel},
     title = {The number of distinct adjacent pairs in geometrically distributed words: a probabilistic and combinatorial analysis},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {25},
     number = {2},
     year = {2023-2024},
     doi = {10.46298/dmtcs.9293},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.9293/}
}
TY  - JOUR
AU  - Louchard, Guy
AU  - Schachinger, Werner
AU  - Ward, Mark Daniel
TI  - The number of distinct adjacent pairs in geometrically distributed words: a probabilistic and combinatorial analysis
JO  - Discrete mathematics & theoretical computer science
PY  - 2023-2024
VL  - 25
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.9293/
DO  - 10.46298/dmtcs.9293
LA  - en
ID  - DMTCS_2024_25_2_a8
ER  - 
%0 Journal Article
%A Louchard, Guy
%A Schachinger, Werner
%A Ward, Mark Daniel
%T The number of distinct adjacent pairs in geometrically distributed words: a probabilistic and combinatorial analysis
%J Discrete mathematics & theoretical computer science
%D 2023-2024
%V 25
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.9293/
%R 10.46298/dmtcs.9293
%G en
%F DMTCS_2024_25_2_a8
Louchard, Guy; Schachinger, Werner; Ward, Mark Daniel. The number of distinct adjacent pairs in geometrically distributed words: a probabilistic and combinatorial analysis. Discrete mathematics & theoretical computer science, Tome 25 (2023-2024) no. 2. doi : 10.46298/dmtcs.9293. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.9293/

Cité par Sources :