Identify real-world objects for coarser-than-permutation-equivalence CRVs

Identify and characterize real-world non-sequential data types that can be modeled as Combinatorial Random Variables defined via equivalence relations coarser than permutation-equivalence, and determine how Random Permutation Codes can be adapted to compress such objects.

Background

Combinatorial Random Variables (CRVs) in the thesis are defined using equivalence relations that are finer than permutation-equivalence, enabling the Random Permutation Codes (RPCs) family to achieve optimal rates efficiently. The authors propose relaxing this restriction to consider equivalence relations coarser than permutation-equivalence, where each equivalence class can be expressed as a disjoint union of permutation-equivalence classes.

While this could allow reusing RPCs as subroutines, the authors explicitly note uncertainty about which real-world non-sequential data types would fit this construction, making it an open modeling question with practical implications for extending RPCs beyond the current framework.