On the grading numbers of direct products of chains

C. C. Chen, K. M. Koh, Sung chul Lee

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

For a finite lattice L, denote by l*(L) and l*(L) respectively the upper length and lower length of L. The grading number g(L) of L is defined as g(L) = l*(Sub(L))-l*(Sub(L)) where Sub(L) is the sublattice-lattice of L. We show that if K is a proper homomorphic image of a distributive lattice L, then l*(Sub(K)) < l*(Sub(L)); and derive from this result, formulae for l*(Sub(L)) and g(L) where L is a product of chains.

Original languageEnglish
Pages (from-to)21-26
Number of pages6
JournalDiscrete Mathematics
Volume49
Issue number1
DOIs
Publication statusPublished - 1984 Jan 1

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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