×

zbMATH — the first resource for mathematics

Valuations on distributive lattices. I, II, III. (English) Zbl 0268.06008
Arch. Math. 24, 230-239 (1973); 24, 337-345 (1973); 24, 475-481 (1973).

MSC:
06D05 Structure and representation theory of distributive lattices
05A99 Enumerative combinatorics
PDF BibTeX Cite
Full Text: DOI
References:
[1] R. Balbes, Projective and injective distributive lattices. Pacific J. Math.21, 405?420 (1967). · Zbl 0157.34301
[2] G.Birkhoff, Lattice Theory. Third ed., Providence 1967.
[3] H.Crapo and G.-C.Rota, Combinatorial Geometries. Cambridge (Mass.) 1970. · Zbl 0216.02101
[4] R. L. Davis, Order Algebras. Bull. Amer. Math. Soc.76, 83?87 (1970). · Zbl 0199.32103
[5] J. Folkman, The homology groups of a lattice. J. Math. Mech.15, 631?636 (1966). · Zbl 0146.01602
[6] L. Geissinger andW. Graves, The category of complete algebraic lattices. J. Combinatorial Theory (A)13, 332?338 (1972). · Zbl 0245.06003
[7] G.Gr?tzer, Lattice Theory. San Francisco 1971.
[8] C.Greene, On the M?bius Algebra of a Partially Ordered Set. Proc. Conf. on M?bius Algebras, University of Waterloo 1971.
[9] P. R.Halmos, Measure Theory. Princeton 1950.
[10] P.Hilton and S.Wylie, Homology Theory. Cambridge 1960.
[11] V. Klee, The Euler characteristic in combinatorial geometry. Amer. Math. Monthly70, 119?127 (1963). · Zbl 0124.37802
[12] A. Horn andA. Tarski, Measures in Boolean algebras. Trans. Amer. Math. Soc.64, 467?497 (1948). · Zbl 0035.03001
[13] R. Larson andM. Sweedler, An associative orthogonal bilinear form for Hopf algebras. Amer. J. Math.91, 75?94 (1969). · Zbl 0179.05803
[14] H. M. MacNeille, Partially ordered sets. Trans. Amer. Math. Soc.42, 416?460 (1937). · JFM 63.0833.04
[15] B. Pettis, Remarks on the extension of lattice functionals. Bull. Amer. Math. Soc.54, 471 (1948).
[16] B. Pettis, On the extension of measures. Ann. of Math.54, 186?197 (1951). · Zbl 0043.27903
[17] H.Rasiowa and R.Sikorski, The Mathematics of Metamathematics. Warsaw 1963. · Zbl 0122.24311
[18] G.-C. Rota, On the foundations of combinatorial theory. I. Z. Wahrscheinlichkeitstheorie Verve. Gebiete2, 340?368 (1964). · Zbl 0121.02406
[19] G.-C.Rota, On the combinatorics of the Euler characteristic. In: Studies in Pure Mathemathics, pp. 221?233. London 1971.
[20] L. Solomon, The Burnside algebra of a finite group. J. Combinatorial Theory2, 603?615 (1967). · Zbl 0183.03601
[21] E.Spanier, Algebraic Topology. New York 1966.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.