On the grading numbers of direct products of chains

C. C. Chen; K. M. Koh; S. C. Lee

doi:10.1016/0012-365X(84)90147-X

On the grading numbers of direct products of chains

C. C. Chen, K. M. Koh, S. C. Lee

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	21-26
Number of pages	6
Journal	Discrete Mathematics
Volume	49
Issue number	1
DOIs	https://doi.org/10.1016/0012-365X(84)90147-X
Publication status	Published - 1984 Mar

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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AU - Koh, K. M.

AU - Lee, S. C.

PY - 1984/3

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N2 - 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.

AB - 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.

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On the grading numbers of direct products of chains

Abstract

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