Geodesic
Groupoid cardinality and random permutations
Theory and applications of categories, Tome 44 (2025), pp. 410-419.

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

If we treat the symmetric group S_n as a probability measure space where each element has measure 1/n!, then the number of cycles in a permutation becomes a random variable. The Cycle Length Lemma describes the expected values of products of these random variables. Here we categorify the Cycle Length Lemma by showing that it follows from an equivalence between groupoids.
Publié le :
Classification : 05A05, 05A19, 20L05
Keywords: groupoid, random permutation, cycle 
@article{TAC_2025_44_a13,
     author = {John C. Baez},
     title = {Groupoid cardinality and random permutations},
     journal = {Theory and applications of categories},
     pages = {410--419},
     publisher = {mathdoc},
     volume = {44},
     year = {2025},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2025_44_a13/}
}
TY  - JOUR
AU  - John C. Baez
TI  - Groupoid cardinality and random permutations
JO  - Theory and applications of categories
PY  - 2025
SP  - 410
EP  - 419
VL  - 44
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TAC_2025_44_a13/
LA  - en
ID  - TAC_2025_44_a13
ER  - 
%0 Journal Article
%A John C. Baez
%T Groupoid cardinality and random permutations
%J Theory and applications of categories
%D 2025
%P 410-419
%V 44
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TAC_2025_44_a13/
%G en
%F TAC_2025_44_a13
John C. Baez. Groupoid cardinality and random permutations. Theory and applications of categories, Tome 44 (2025), pp. 410-419. http://geodesic.mathdoc.fr/item/TAC_2025_44_a13/