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Henry Crapo (mathematician)

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Henry Crapo
Henry Crapo at Oberwolfach in 1987
Henry Howland Crapo

(1932-08-12)August 12, 1932
Detroit, Michigan, United States
DiedSeptember 3, 2019(2019-09-03) (aged 87)
CitizenshipAmerican, Canadian
Alma materMassachusetts Institute of Technology (Ph.D.)
Known forMatroid theory
Scientific career
ThesisOn the Theory of Combinatorial Independence (1964)
Doctoral advisorsGian-Carlo Rota, Kenneth Hoffman

Henry Howland Crapo (KRAY-poh;[1] August 12, 1932 – September 3, 2019) was an American-Canadian mathematician who worked in algebraic combinatorics. Over the course of his career, he held positions at several universities and research institutes in Canada and France. He is noted for his work in matroid theory and lattice theory.

Education and career[edit]

Crapo was born in Detroit, Michigan, in 1932.[2][3] He received his Ph.D. in 1964 under the supervision of Gian-Carlo Rota and Kenneth Hoffman, with thesis On the theory of combinatorial independence.[4][5] While working on his thesis, he was an Assistant Professor at Northeastern University in Boston.[5][6] He subsequently held academic positions at the University of Waterloo, Université de Montréal, INRIA Rocquencourt, and École des Hautes Études en Sciences Sociales.[7] During his time in Waterloo, Crapo became a Canadian citizen.[3]

Crapo is known for his early work in matroid theory, and for related work in lattice theory. He introduced the beta invariant of a matroid,[8] and published the first paper on the Tutte polynomial[9] (though Tutte had already defined an equivalent polynomial in his thesis). Together with Gian-Carlo Rota, Crapo wrote the first book on matroid theory.[10][11] He is also known for Crapo's Complementation Theorem in poset Möbius Inversion.[12][13] Crapo wrote 65 mathematical publications during his career.[14]

Upon his retirement, Crapo moved to the south of France.[3] He continued some mathematical activity, and hosted several small conferences at his house there.[11] He died on September 3, 2019.[15]

Awards and honors[edit]

Personal life[edit]

a large bronze statue of boar
The University of Waterloo Porcellino, donated by Crapo

Crapo was a patron of the arts. At the University of Waterloo he donated a collection of rare books on the history of dance and ballet,[17] as well as a copy of the Porcellino sculpture of Florence; the latter shoulder-high bronze sculpture of a wild boar later became a mascot for the University of Waterloo Faculty of Arts.[18] He also donated The Temptation of St. Anthony by James Ensor to the Royal Museum of Fine Arts in Antwerp[3] and Corpse of Man by Hyman Bloom to the Rose Art Museum at Brandeis University.[19]


  1. ^ "Pronunciation: Crapo". MathOverflow. Retrieved October 25, 2019.
  2. ^ "Remembering Henry Crapo". uwaterloo.ca. University of Waterloo. October 25, 2019. Retrieved October 31, 2019.
  3. ^ a b c d "Maths Genius Donates James Ensor Painting". Collection. Royal Museum of Fine Arts Antwerp. Retrieved October 25, 2019.
  4. ^ Henry Howland Crapo at the Mathematics Genealogy Project
  5. ^ a b Crapo, Henry H. (1964). On the theory of combinatorial independence (Thesis). Massachusetts Institute of Technology.
  6. ^ Crapo, Henry H. (1965), "Single-element extensions of matroids", J. Res. Nat. Bur. Standards Sect. B, 69 B: 55–65, MR 0190045
  7. ^ a b Kung, Joseph P.S. (1999). "Guest Editor's Introduction". Advances in Applied Mathematics. 23 (1). Elsevier: 1–2. doi:10.1006/aama.1999.0642. ISSN 0196-8858.
  8. ^ Crapo, Henry H. (1967). "A higher invariant for matroids". Journal of Combinatorial Theory. 2 (4). Elsevier: 406–417. doi:10.1016/s0021-9800(67)80051-6. ISSN 0021-9800. MR 0215744.
  9. ^ Crapo, Henry H. (1969). "The Tutte polynomial". Aequationes Mathematicae. 3 (3). Springer Science and Business Media LLC: 211–229. doi:10.1007/bf01817442. ISSN 0001-9054. MR 0215744. S2CID 119602825.
  10. ^ Crapo, Henry; Rota, Gian-Carlo (1970). On the Foundations of Combinatorial Theory: Combinatorial Geometries. Cambridge, Massachusetts: M.I.T. Press. ISBN 978-0-262-53016-3. MR 0290980. OCLC 117282.
  11. ^ a b Oxley, James. "Henry Crapo: A Brief Reminiscence". Matroid Union.
  12. ^ Crapo, Henry H. (1966). "The Möbius function of a lattice". Journal of Combinatorial Theory. 1 (1). Elsevier BV: 126–131. doi:10.1016/s0021-9800(66)80009-1. ISSN 0021-9800. MR 0193018.
  13. ^ Stanley, Richard (2012). Enumerative combinatorics. New York: Cambridge University Press. ISBN 978-1-107-60262-5. MR 2868112. OCLC 777400915.
  14. ^ "Henry H. Crapo author profile". MathSciNet. American Mathematical Society.
  15. ^ "Henry Crapo Death Notice" (in French). Retrieved October 25, 2019.
  16. ^ Penne, Rudi (1999). "Almost Flat Line Configurations". Advances in Applied Mathematics. 23 (1). Elsevier: 54–77. doi:10.1006/aama.1999.0647. ISSN 0196-8858. MR 1692976.
  17. ^ "Crapo, Henry H." Special Collections & Archives. University of Waterloo Library. Retrieved October 25, 2019.
  18. ^ "The Boar in the News". Special Collections & Archives. University of Waterloo Library. March 6, 2015. Retrieved October 25, 2019.
  19. ^ "Corpse of Man". rosecollection.brandeis.edu. Rose Art Museum. Retrieved March 27, 2024.