A method and apparatus is provided for implementing combinatorial hypermaps (CHYMAPS) and/or generalized combinatorial maps (G-Maps) based data representations and operations, comprising: mapping term-algebras to tree-based numbers using a fast algorithm and representing a graph of the mapping structure as a CHYMAPS using reversible numeric encoding and decoding; generating a representation of CHYMAPS in a form optimized for sub-map (sub-graph) to map (graph) isomorphism and partial matching with a general matching process; performing operations on the CHYMAPS as operations on respective numerical representations; performing compression and decompression using a three bit self-delimiting binary code; and storing and retrieving codes.