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Counting formulas for glued lattices (1985)

Reuter, Klaus

Springer

Order 1 (1985), S. 265-276

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ISSN: 1572-9273

Keywords: 05A15 ; 06B05 ; Incidence structure ; graph ; glued lattice ; glued tolerance relation ; skeleton ; Dilworth's theorem

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract A tolerance relation θ of a lattice L, i.e., a reflexive and symmetric relation of L which is compatible with join and meet, is called glued if covering blocks of θ have nonempty intersection. For a lattice L with a glued tolerance relation we prove a formula counting the number of elements of L with exactly k lower (upper) covers. Moreover, we prove similar formulas for incidence structures and graphs and we give a new proof of Dilworth's covering theorem.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF00383603

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