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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2512.03367 |
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Table des matières:
- Tom Leinster gave a bijective correspondence between the set of operators on a finite-dimensional vector space $V$ and the set of pairs consisting of a nilpotent operator and a vector in $V$. Over a finite field this bijection implies that the probability that an operator be nilpotent is the reciprocal of the number of vectors in $V$. We generalize this correspondence to pairs of operators between pairs of vector spaces and determine the probability that a random pair of operators be nilpotent. We also determine the set-theoretical counterpart of this construction and compute the number of eventually constant pairs of maps between two finite sets, closely related to the number of spanning trees in a complete bipartite graph.