On some combinatorial properties of the orbits on subsets

2010/04/14 by Xavier Buchwalder, Buchwalder, Xavier
Computer Science · Engineering · #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #graph theory and CDMA systems #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1004.2375

openalex publication_date 2010/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce generalised orbit algebras. The purpose here is to measure how some combinatorial properties can characterize the action of a group of permutations on the subsets. The similarity with orbit algebras is such that it took the author a long time to find a generalised orbit algebra not arising from a permutation group.

Related

• Finite Permutation Groups with Few Orbits Under the Action on the Power Set
• On the orbit-sizes of permutation groups containing elements separating finite subsets
• The orbit algebra of a permutation group with polynomial profile is Cohen-Macaulay
• Permutation Groups and Orbits on Power Sets
• Orbits and self-twuality in set systems and delta-matroids