Abstract
Inspired by engineering of high-speed switching with quality of service, this paper introduces a new approach to classify finite lattices by the concept of cut-through coding. An n-ary cut-through code of a finite lattice encodes all lattice elements by distinct n-ary strings of a uniform length such that for all j, the initial j encoding symbols of any two elements x and y determine the initial j encoding symbols of the meet and join of x and y. In terms of lattice congruences, some basic criteria are derived to characterize the n-ary cut-through codability of a finite lattice. N-ary cut-through codability also gives rise to a new classification of lattice varieties and in particular, defines a chain of ideals in the lattice of lattice varieties.
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This work was supported in part by the National Natural Science Foundation of China (Grant No. 61201261), China 973 Programs No. 2012CB315901 & 2012CB315904, and AoE grant E-02/08 from the University Grants Committee of Hong Kong SAR.
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Sun, Q.T., Li, SY.R. Lattice Classification by Cut-through Coding. Order 31, 271–278 (2014). https://doi.org/10.1007/s11083-013-9300-x
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DOI: https://doi.org/10.1007/s11083-013-9300-x