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Bill Sands

photograph of Bill Sands

Job Title:

  • Professor

Phone:

  • +1 (403) 220-6310

Office:

  • MS 566

Email:

Web site:

Degrees:

Research Interests:

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

Ph. D. Student:

  • Jia Shen (2008)

Teaching:

Past Courses:

  • MATH221 - LINEAR ALGEBRA FOR SCIENCE & ENGG
  • MATH249 - INTRODUCTORY CALCULUS
  • MATH251 - CALCULUS I
  • MATH271 - Discrete Mathematics
  • PMAT315 - Abstract Algebra
  • PMAT371 - COMBINATORIAL MATHEMATICS
  • PMAT421 - INTRODUCTION TO COMPLEX ANALYSIS
  • PMAT431 - GROUPS, RINGS AND FIELDS
Representative Publications:
Preprint
Sands, Bill and Duffus, Dwight. "Finite distributive lattices and the splitting property." (March 2002)
Journal Paper
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
Duffus, Dwight and Sands, Bill. "Finite distributive lattices and the splitting property" Algebra Universalis 49.1 (2003): 13-33
Paulhus, 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
Duffus, Dwight and Sands, Bill. "Minimum sized fibres in distributive lattices" Journal of the Australian Mathematical Society 70.3 (2001): 337-350
Ginsburg, John and Sands, Bill. "An optimal algorithm for a parallel cutting problem" Ars Combinatoria 57 (2000): 87-95
Ginsburg, John and Sands, Bill. "Completely disconnecting the complete graph" SIAM Journal on Discrete Mathematics 13.1 (2000): 33-47 (electronic)
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
Linek, V. and Sands, Bill. "A note on paths in edge-coloured tournaments" Ars Combinatoria 44 (1996): 225-228
Duffus, Dwight, R{\"o}dl, Vojt , Sands, Bill and Woodrow, Robert. "Enumeration of order preserving maps" Order 9.1 (1992): 15-29
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
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
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
Duffus, Dwight, Sands, Bill and Woodrow, Robert. "Lexicographic matchings cannot form {H}amiltonian cycles" Order 5.2 (1988): 149-161
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
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
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
Ruckelshausen, W. and Sands, Bill. "On finitely generated lattices of width four" Algebra Universalis 16.1 (1983): 17-37
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
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
Sands, Bill. "Counting antichains in finite partially ordered sets" Discrete Math. 35 (1981): 213-228
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
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
Sands, Bill. "Generating sets for lattices of dimension two" Discrete Math. 29.3 (1980): 287-292
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
Ginsburg, John and Sands, Bill. "Minimal infinite topological spaces" The American Mathematical Monthly 86.7 (1979): 574-576
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
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
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
Kucera, T. G. and Sands, Bill. "Lattices of lattice homomorphisms" Algebra Universalis 8.2 (1978): 180-190
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
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
Sands, Bill. "On a problem involving bounded epimorphisms of lattices" Algebra Universalis 7.2 (1977): 211-217
Yao, Andrew C. C., Reingold, Edward M. and Sands, Bill. "Tiling with incomparable rectangles" J. Recreational Math. 8.2 (1975/76): 112-119
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
Book
Rival, Ivan and Sands, Bill. Pictures in lattice theory 65, North-Holland (1982): 341-355
Rival, Ivan and Sands, Bill. How many four-generated simple lattices? 9, PWN (1982): 67-72

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