On extendability of permutations
Mark Pankov

TL;DR
This paper characterizes finite subsets of vector spaces and projective spaces where all permutations can be extended to linear automorphisms or projective transformations, linking the results to symmetric group representations.
Contribution
It provides a complete description of subsets allowing permutation extensions to automorphisms or projective transformations, connecting to symmetric group representations.
Findings
Characterization of subsets with permutation extension property
Description of subsets in projective space with permutation extension
Reformulation in terms of symmetric group representations
Abstract
Let be a left vector space over a division ring and let be the associated projective space. We describe all finite subsets such that every permutation on can be extended to a linear automorphism of and all finite subsets such that every permutation on can be extended to an element of . Also, we reformulate the results in terms of linear and projective representations of symmetric groups.
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Taxonomy
TopicsFinite Group Theory Research · Coding theory and cryptography · Cooperative Communication and Network Coding
