# Bill Sands

#### Professor Emeritus

#### PhD

#### MSc

#### BSc

## Contact information

#### Phone

#### Location

## Research and teaching

### Research areas

- Enumeration in partial orders and lattices
- Edge colouring in graphs
- Cutsets and fibres in partial orders

## Publications

### Book

*Rival, Ivan and Sands, Bill*. Pictures in lattice theory 65. North-Holland, 1982. 341-355. Print.*Rival, Ivan and Sands, Bill*. How many four-generated simple lattices? 9. PWN, 1982. 67-72. Print.

### Journal article

*Sauer, Norbert, Sands, Bill, Duffus, Dwight and V. Rodl*. "Chromatic numbers and homomorphisms of large girth hypergraphs". Algorithms and Combinatorics, Topics in Discrete Mathematics 26. (2006): 455-471. Print.*Duffus, Dwight and Sands, Bill*. "Finite distributive lattices and the splitting property". Algebra Universalis 49.1 (2003): 13-33. Print.*Duffus, Dwight and Sands, Bill*. "Minimum sized fibres in distributive lattices". Journal of the Australian Mathematical Society 70.3 (2001): 337-350. Print.*Paulhaus, Marc and Sands, Bill*. "Nonregular graphs with a regular number of walks". Bulletin of the Institute of Combinatorics and its Applications 32. (2001): 77-89. Print.*Ginsburg, John and Sands, Bill*. "An optimal algorithm for a parallel cutting problem". Ars Combinatoria 57. (2000): 87-95. Print.*Ginsburg, John and Sands, Bill*. "Completely disconnecting the complete graph". SIAM Journal on Discrete Mathematics 13.1 (2000): 33-47 (electronic). Print.*Duffus, Dwight and Sands, Bill*. "An inequality for the sizes of prime filters of finite distributive lattices". Discrete Math. 201.1-3 (1999): 89-99. Print.*Linek, V. and Sands, Bill*. "A note on paths in edge-coloured tournaments". Ars Combinatoria 44. (1996): 225-228. Print.*Duffus, Dwight, R{\"o}dl, Vojt, Sands, Bill and Woodrow, Robert*. "Enumeration of order preserving maps". Order 9.1 (1992): 15-29. Print.*Duffus, Dwight, Sands, Bill, Sauer, Norbert and Woodrow, Robert*. "Two-colouring all two-element maximal antichains". Journal of Combinatorial Theory. Series A 57.1 (1991): 109-116. Print.*Duffus, Dwight, Sands, Bill and Winkler, P.*. "Maximal chains and antichains in {B}oolean lattices". SIAM Journal on Discrete Mathematics 3.2 (1990): 197-205. Print.*Ginsburg, John, Sands, Bill and West, Douglas B.*. "A length-width inequality for partially ordered sets with two-element cutsets". Journal of Combinatorial Theory. Series B 46.2 (1989): 232-239. Print.*Duffus, Dwight, Sands, Bill and Woodrow, Robert*. "Lexicographic matchings cannot form {H}amiltonian cycles". Order 5.2 (1988): 149-161. Print.*Ginsburg, J., Rival, I. and Sands, Bill*. "Antichains and finite sets that meet all maximal chains". Canadian Journal of Mathematics. Journal Canadien de Math\'ematiques 38.3 (1986): 619-632. Print.*Faigle, U. and Sands, Bill*. "A size-width inequality for distributive lattices". Combinatorica. An International Journal of the J\'anos Bolyai Mathematical Society 6.1 (1986): 29-33. Print.*Duffus, Dwight, Sands, Bill and Woodrow, Robert*. "On the chromatic number of the product of graphs". Journal of Graph Theory 9.4 (1985): 487-495. Print.*Ruckelshausen, W. and Sands, Bill*. "On finitely generated lattices of width four". Algebra Universalis 16.1 (1983): 17-37. Print.*Sands, Bill, Sauer, Norbert and Woodrow, Robert*. "On monochromatic paths in edge-coloured digraphs". Journal of Combinatorial Theory. Series B 33.3 (1982): 271-275. Print.*Galvin, F., Rival, I. and Sands, Bill*. "A {R}amsey-type theorem for traceable graphs". Journal of Combinatorial Theory. Series B 33.1 (1982): 7-16. Print.*Rival, I., Ruckelshausen, W. and Sands, Bill*. "On the ubiquity of herringbones in finitely generated lattices". Proc. Amer. Math. Soc. 82.3 (1981): 335-340. Print.*Sands, Bill*. "Counting antichains in finite partially ordered sets". Discrete Math. 35. (1981): 213-228. Print.*Poguntke, W. and Sands, Bill*. "On finitely generated lattices of finite width". Canadian Journal of Mathematics. Journal Canadien de Math\'ematiques 33.1 (1981): 28-48. Print.*Sands, Bill*. "Generating sets for lattices of dimension two". Discrete Math. 29.3 (1980): 287-292. Print.*Rival, Ivan and Sands, Bill*. "On the adjacency of vertices to the vertices of an infinite subgraph". Journal of the London Mathematical Society. Second Series 21.3 (1980): 393-400. Print.*Gr{\"a}tzer, G., Platt, C. R. and Sands, Bill*. "Embedding lattices into lattices of ideals". Pacific Journal of Mathematics 85.1 (1979): 65-75. Print.*Ginsburg, John and Sands, Bill*. "Minimal infinite topological spaces". The American Mathematical Monthly 86.7 (1979): 574-576. Print.*Rival, Ivan and Sands, Bill*. "Planar sublattices of a free lattice. {II}". Canadian Journal of Mathematics. Journal Canadien de Math\'ematiques 31.1 (1979): 17-34. Print.*Rival, Ivan and Sands, Bill*. "A note on the congruence lattice of a finitely generated algebra". Proc. Amer. Math. Soc. 72.3 (1978): 451-455. Print.*Rival, Ivan and Sands, Bill*. "Planar sublattices of a free lattice. {I}". Canadian Journal of Mathematics. Journal Canadien de Math\'ematiques 30.6 (1978): 1256-1283. Print.*Kucera, T. G. and Sands, Bill*. "Lattices of lattice homomorphisms". Algebra Universalis 8.2 (1978): 180-190. Print.*Sands, Bill*. "On a problem involving bounded epimorphisms of lattices". Algebra Universalis 7.2 (1977): 211-217. Print.*Davey, Brian A. and Sands, Bill*. "An application of {W}hitman's condition to lattices with no infinite chains". Algebra Universalis 7.2 (1977): 171-178. Print.*Yao, Andrew C. C., Reingold, Edward M. and Sands, Bill*. "Tiling with incomparable rectangles". J. Recreational Math. 8.2 (1975/76): 112-119. Print.*Rival, Ivan and Sands, Bill*. "Weak embeddings and embeddings of finite distributive lattices". Archiv der Mathematik. Archives of Mathematics. Archives Math\'ematiques 26.4 (1975): 346-352. Print.

### Preprint

*Sands, Bill and Duffus, Dwight*. "Finite distributive lattices and the splitting property.". , (March 2002). Print.