Henry Howland Crapo (; August 12, 1932 – September 3, 2019) was an American-Canadian mathematician who worked in

algebraic combinatorics Algebraic combinatorics is an area of mathematics that employs methods of abstract algebra, notably group theory and representation theory, in various combinatorial contexts and, conversely, applies combinatorial techniques to problems in algeb ...

. 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 In combinatorics, a matroid is a structure that abstracts and generalizes the notion of linear independence in vector spaces. There are many equivalent ways to define a matroid Axiomatic system, axiomatically, the most significant being in terms ...

and

lattice theory A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra. It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a least upper bou ...

Education and career

Crapo was born in

Detroit Detroit ( , ) is the List of municipalities in Michigan, most populous city in the U.S. state of Michigan. It is situated on the bank of the Detroit River across from Windsor, Ontario. It had a population of 639,111 at the 2020 United State ...

Michigan Michigan ( ) is a peninsular U.S. state, state in the Great Lakes region, Great Lakes region of the Upper Midwest, Upper Midwestern United States. It shares water and land boundaries with Minnesota to the northwest, Wisconsin to the west, ...

, in 1932. He received his Ph.D. in 1964 under the supervision of

Gian-Carlo Rota Gian-Carlo Rota (April 27, 1932 – April 18, 1999) was an Italian-American mathematician and philosopher. He spent most of his career at the Massachusetts Institute of Technology, where he worked in combinatorics, functional analysis, proba ...

and Kenneth Hoffman, with thesis ''On the theory of combinatorial independence''. While working on his thesis, he was an assistant professor at

Northeastern University Northeastern University (NU or NEU) is a private university, private research university with its main campus in Boston, Massachusetts, United States. It was founded by the Boston Young Men's Christian Association in 1898 as an all-male instit ...

Boston Boston is the capital and most populous city in the Commonwealth (U.S. state), Commonwealth of Massachusetts in the United States. The city serves as the cultural and Financial centre, financial center of New England, a region of the Northeas ...

. He subsequently held academic positions at the

University of Waterloo The University of Waterloo (UWaterloo, UW, or Waterloo) is a Public university, public research university located in Waterloo, Ontario, Canada. The main campus is on of land adjacent to uptown Waterloo and Waterloo Park. The university also op ...

Université de Montréal The Université de Montréal (; UdeM; ) is a French-language public research university in Montreal, Quebec, Canada. The university's main campus is located in the Côte-des-Neiges neighborhood of Côte-des-Neiges–Notre-Dame-de-Grâce on M ...

INRIA The National Institute for Research in Digital Science and Technology (Inria) () is a French national research institution focusing on computer science and applied mathematics. It was created under the name French Institute for Research in Comp ...

Rocquencourt, and

École des Hautes Études en Sciences Sociales The School for Advanced Studies in the Social Sciences (, EHESS) is a graduate ''grande école'' and '' grand établissement'' in Paris focused on academic research in the social sciences. The school awards Master and PhD degrees alone and conj ...

. During his time in Waterloo, Crapo became a Canadian citizen. Crapo is known for his early work in

matroid In combinatorics, a matroid is a structure that abstracts and generalizes the notion of linear independence in vector spaces. There are many equivalent ways to define a matroid Axiomatic system, axiomatically, the most significant being in terms ...

theory, and for related work in lattice theory. He introduced the beta invariant of a matroid, and published the first paper on the

Tutte polynomial The Tutte polynomial, also called the dichromate or the Tutte–Whitney polynomial, is a graph polynomial. It is a polynomial in two variables which plays an important role in graph theory. It is defined for every undirected graph G and contai ...

(though Tutte had already defined an equivalent polynomial in his thesis). Together with Gian-Carlo Rota, Crapo wrote the first book on matroid theory. He is also known for Crapo's Complementation Theorem in poset Möbius Inversion. Crapo wrote 65 mathematical publications during his career. Upon his retirement, Crapo moved to the south of

France France, officially the French Republic, is a country located primarily in Western Europe. Overseas France, Its overseas regions and territories include French Guiana in South America, Saint Pierre and Miquelon in the Atlantic Ocean#North Atlan ...

. He continued some mathematical activity, and hosted several small conferences at his house there. He died on September 3, 2019.

Awards and honors

* A special 1999 issue of the journal ''

Advances in Applied Mathematics ''Advances in Applied Mathematics'' is a peer-reviewed mathematics journal publishing research on applied mathematics. Its founding editor was Gian-Carlo Rota (Massachusetts Institute of Technology); from 1980 to 1999, Joseph P. S. Kung (Universi ...

'' was dedicated to Crapo on the occasion of his 67th birthday.

Personal life

Crapo was a patron of the arts. At the

he donated a collection of rare books on the history of dance and ballet, as well as a copy of the

Porcellino (Italian "piglet") is the local Florentine nickname for the bronze fountain of a boar. The fountain figure was sculpted and cast by Baroque master Pietro Tacca (1577–1640) shortly before 1634, following a marble Italian copy of a Hellenisti ...

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 The Faculty of Arts is one of six faculties at the University of Waterloo in Waterloo, Ontario, Canada. Departments The faculty presently houses sixteen academic departments, the School of Accounting and Finance and the Stratford School of In ...

. He also donated ''The Temptation of St. Anthony'' by

James Ensor James Sidney Edouard, Baron Ensor (13 April 1860 – 19 November 1949) was a Belgian painter and printmaker, an important influence on expressionism and surrealism who lived in Ostend for most of his life. He was associated with the artistic ...

to the Royal Museum of Fine Arts in Antwerp and ''Corpse of Man'' by

Hyman Bloom Hyman Bloom (March 29, 1913 – August 26, 2009) was a Latvian-born American painter. His work was influenced by his Jewish heritage and Eastern religions as well as by artists including Altdorfer, Grünewald, Caravaggio, Rembrandt, Blake, Br ...

to the

Rose Art Museum The Rose Art Museum, founded in 1961, is a part of Brandeis University in Waltham, Massachusetts, US. Named after benefactors Edward and Bertha Rose, it offers temporary exhibitions, and it displays and houses works of art from its permanent co ...

Brandeis University Brandeis University () is a Private university, private research university in Waltham, Massachusetts, United States. It is located within the Greater Boston area. Founded in 1948 as a nonsectarian, non-sectarian, coeducational university, Bra ...

References

{{DEFAULTSORT:Crapo, Henry 1932 births 2019 deaths 20th-century American mathematicians 21st-century American mathematicians 20th-century Canadian mathematicians 21st-century Canadian mathematicians Massachusetts Institute of Technology School of Science alumni Northeastern University faculty Academic staff of the University of Waterloo Academic staff of the Université de Montréal Combinatorialists Scientists from Detroit Writers from Detroit Mathematicians from Michigan Naturalized citizens of Canada Canadian expatriates in France American expatriates in France