The Twelvefold Way of Non-Sequential Lossless Compression

Taha Ameen ur Rahman, Alton S. Barbehenn, Xinan Chen, Hassan Dbouk, James A. Douglas, Yuncong Geng, Ian George, John B. Harvill, Sung Woo Jeon, Kartik K. Kansal, Kiwook Lee, Kelly A. Levick, Bochao Li, Ziyue Li, Yashaswini Murthy, Adarsh Muthuveeru-Subramaniam, S. Yagiz Olmez, Matthew J. Tomei, Tanya Veeravalli, Xuechao Wang et al. (10 additional authors not shown)

Abstract: Many information sources are not just sequences of distinguishable symbols but rather have invariances governed by alternative counting paradigms such as permutations, combinations, and partitions. We consider an entire classification of these invariances called the twelvefold way in enumerative combinatorics and develop a method to characterize lossless compression limits. Explicit computations for all twelve settings are carried out for i.i.d. uniform and Bernoulli distributions. Comparisons among settings provide quantitative insight.