, Volume 31, Issue 2, pp 271–278 | Cite as

Lattice Classification by Cut-through Coding

  • Qifu Tyler Sun
  • Shuo-Yen Robert Li


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.


Cut-through coding Finite lattice Lattice congruence Lattice variety 


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Institute of Network Coding (Shenzhen), Shenzhen Research InstituteThe Chinese University of Hong KongShenzhenChina
  2. 2.Department of Information Engineering and Institute of Network CodingThe Chinese University of Hong KongNew TerritoriesHong Kong

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