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Lattice Classification by Cut-through Coding

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An Erratum to this article was published on 09 March 2014

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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Authors and Affiliations

  1. Institute of Network Coding (Shenzhen), Shenzhen Research Institute, The Chinese University of Hong Kong, Shenzhen, China

    Qifu Tyler Sun

  2. Department of Information Engineering and Institute of Network Coding, The Chinese University of Hong Kong, New Territories, Hong Kong

    Shuo-Yen Robert Li

Authors
  1. Qifu Tyler Sun
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  2. Shuo-Yen Robert Li
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Corresponding author

Correspondence to Qifu Tyler Sun.

Additional information

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

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