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**Thomas Zaslavsky** (born 1945) is an American mathematician specializing in combinatorics.

A **mathematician** is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.

**Combinatorics** is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics, from evolutionary biology to computer science, etc.

Zaslavsky's mother Claudia Zaslavsky was a high school mathematics teacher in New York; his father Sam Zaslavsky (from Manhattan) was an electrical engineer. Thomas Zaslavsky graduated from the City College of New York. At M.I.T. he studied hyperplane arrangements with Curtis Greene and received a Ph.D. in 1974. In 1975 the American Mathematical Society published his doctoral thesis.

**Claudia Zaslavsky** was an American educator and ethnomathematician. She advanced the study of the links between mathematics and world cultures, especially with her pioneering book *Africa Counts*, that extended to Africa the work of Karl Menninger about mathematics in ordinary life in other parts of the world. She also worked to advance multicultural mathematics teaching with books and articles and by personal activity. Her son Thomas Zaslavsky is a mathematician in the U.S. and her son Alan Zaslavsky is a statistician at Harvard Medical School.

**Manhattan**, often referred to as * the City*, is the most densely populated of the five boroughs of New York City, and coextensive with the

The **City College of the City University of New York** is a public senior college of the City University of New York (CUNY) in New York City. Founded in 1847, City College was the first free public institution of higher education in the United States. It is the oldest of CUNY's 24 institutions of higher learning, and is considered its flagship college.

Zaslavsky has been a professor of mathematics at the Binghamton University, New York since 1985. He has published papers on matroid theory and has made available a bibliography on signed graphs and their applications. He has also written on coding theory, lattice point counting, and Sperner theory.

**Mathematics** includes the study of such topics as quantity, structure (algebra), space (geometry), and change. It has no generally accepted definition.

The **State University of New York at Binghamton**, commonly referred to as **Binghamton University** and **SUNY Binghamton**, is a public research university with campuses in Binghamton, Vestal, and Johnson City, New York. It is one of the four university centers in the State University of New York (SUNY) system. As of Fall 2018, 17,768 undergraduate and graduate students attend the university. The Vestal campus is listed as a census-designated place, with a residential population of 6,177 as of the 2010 Census.

**New York** is a state located in the Northeastern United States. New York was one of the original thirteen colonies that formed the United States. With an estimated 19.54 million residents in 2018, it is the fourth most populous state. In order to distinguish the state from its city with the same name, it is sometimes referred to as **New York State** (**NYS**).

- 2015: Bibliography, glossary, and problem list for signed, gained, and biased graphs from Binghamton University.
- 2003: "Faces of a hyperplane arrangement enumerated by ideal dimension, with application to plane, plaids, and Shi", Geometriae Dedicata 98: 63–80.
- 1983: (with Curtis Greene) "On the interpretation of Whitney numbers through arrangements of hyperplanes, zonotopes, non-Radon partitions, and orientations of graphs", Transactions of the American Mathematical Society 280(1): 97–126, doi : 10.2307/1999604 MR 712251.
- 1975:
*Facing up to Arrangements: Face-count Formulas for Partitions of Space by Hyperplanes*, Memoirs of the American Mathematical Society, Google Books preview.

* Geometriae Dedicata* is a mathematical journal, founded in 1972, concentrating on geometry and its relationship to topology, group theory and the theory of dynamical systems. It was created on the initiative of Hans Freudenthal in Utrecht, the Netherlands. It is published by Springer Netherlands. The Editors-in-Chief are John R. Parker and Jean-Marc Schlenker.

The * Transactions of the American Mathematical Society* is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society. It was established in 1900. As a requirement, all articles must be more than 15 printed pages.

In computing, a **digital object identifier** (**DOI**) is a persistent identifier or handle used to identify objects uniquely, standardized by the International Organization for Standardization (ISO). An implementation of the Handle System, DOIs are in wide use mainly to identify academic, professional, and government information, such as journal articles, research reports and data sets, and official publications though they also have been used to identify other types of information resources, such as commercial videos.

In combinatorics, a branch of mathematics, 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, the most significant being in terms of independent sets, bases, circuits, closed sets or flats, closure operators, and rank functions.

In the mathematical theory of matroids, a **graphic matroid** is a matroid whose independent sets are the forests in a given finite undirected graph. The dual matroids of graphic matroids are called **co-graphic matroids** or **bond matroids**. A matroid that is both graphic and co-graphic is called a **planar matroid**; these are exactly the graphic matroids formed from planar graphs.

In geometry and combinatorics, an **arrangement of hyperplanes** is an arrangement of a finite set *A* of hyperplanes in a linear, affine, or projective space *S*. Questions about a hyperplane arrangement *A* generally concern geometrical, topological, or other properties of the **complement**, *M*(*A*), which is the set that remains when the hyperplanes are removed from the whole space. One may ask how these properties are related to the arrangement and its intersection semilattice. The **intersection semilattice** of *A*, written *L*(*A*), is the set of all subspaces that are obtained by intersecting some of the hyperplanes; among these subspaces are *S* itself, all the individual hyperplanes, all intersections of pairs of hyperplanes, etc.. These subspaces are called the **flats** of *A*. The intersection semilattice *L*(*A*) is partially ordered by *reverse inclusion*.

**Frank Harary** was an American mathematician, who specialized in graph theory. He was widely recognized as one of the "fathers" of modern graph theory. Harary was a master of clear exposition and, together with his many doctoral students, he standardized the terminology of graphs. He broadened the reach of this field to include physics, psychology, sociology, and even anthropology. Gifted with a keen sense of humor, Harary challenged and entertained audiences at all levels of mathematical sophistication. A particular trick he employed was to turn theorems into games - for instance, students would try to add red edges to a graph on six vertices in order to create a red triangle, while another group of students tried to add edges to create a blue triangle. Because of the theorem on friends and strangers, one team or the other would have to win.

**Branko Grünbaum** was a Yugoslavian-born mathematician of Jewish descent and a professor emeritus at the University of Washington in Seattle. He received his Ph.D. in 1957 from Hebrew University of Jerusalem in Israel.

In the area of graph theory in mathematics, a **signed graph** is a graph in which each edge has a positive or negative sign.

In mathematics, a **biased graph** is a graph with a list of distinguished circles, such that if two circles in the list are contained in a theta graph, then the third circle of the theta graph is also in the list. A biased graph is a generalization of the combinatorial essentials of a gain graph and in particular of a signed graph.

**Geometric graph theory** in the broader sense is a large and amorphous subfield of graph theory, concerned with graphs defined by geometric means. In a stricter sense, geometric graph theory studies combinatorial and geometric properties of geometric graphs, meaning graphs drawn in the Euclidean plane with possibly intersecting straight-line edges, and topological graphs, where the edges are allowed to be arbitrary continuous curves connecting the vertices, thus it is "the theory of geometric and topological graphs".

**Mathematical sociology** is the area of sociology that uses mathematics to construct social theories. Mathematical sociology aims to take sociological theory, which is strong in intuitive content but weak from a formal point of view, and to express it in formal terms. The benefits of this approach include increased clarity and the ability to use mathematics to derive implications of a theory that cannot be arrived at intuitively. In mathematical sociology, the preferred style is encapsulated in the phrase "constructing a mathematical model." This means making specified assumptions about some social phenomenon, expressing them in formal mathematics, and providing an empirical interpretation for the ideas. It also means deducing properties of the model and comparing these with relevant empirical data. Social network analysis is the best-known contribution of this subfield to sociology as a whole and to the scientific community at large. The models typically used in mathematical sociology allow sociologists to understand how predictable local interactions are and they are often able to elicit global patterns of social structure.

A **gain graph** is a graph whose edges are labelled "invertibly", or "orientably", by elements of a group *G*. This means that, if an edge *e* in one direction has label *g*, then in the other direction it has label *g*^{ −1}. The label function *φ* therefore has the property that it is defined differently, but not independently, on the two different orientations, or directions, of an edge *e*. The group *G* is called the **gain group**, *φ* is the **gain function**, and the value *φ*(*e*) is the **gain** of *e*. A gain graph is a generalization of a signed graph, where the gain group *G* has only two elements. See Zaslavsky.

**Peter John Hilton** was a British mathematician, noted for his contributions to homotopy theory and for code-breaking during the Second World War.

**George Jiří Klir** was a Czech-American computer scientist and professor of systems sciences at Binghamton University in Binghamton, New York.

**Martin Charles Golumbic** is a mathematician and computer scientist, best known for his work in algorithmic graph theory and in artificial intelligence. He is the founding editor-in-chief of the journal *Annals of Mathematics and Artificial Intelligence*.

In graph theory, a branch of mathematics, a **skew-symmetric graph** is a directed graph that is isomorphic to its own transpose graph, the graph formed by reversing all of its edges, under an isomorphism that is an involution without any fixed points. Skew-symmetric graphs are identical to the double covering graphs of bidirected graphs.

**András Hajnal** was a professor of mathematics at Rutgers University and a member of the Hungarian Academy of Sciences known for his work in set theory and combinatorics.

**Norman Linstead Biggs** is a leading British mathematician focusing on discrete mathematics and in particular algebraic combinatorics.

In geometry, the **moment curve** is an algebraic curve in *d*-dimensional Euclidean space given by the set of points with Cartesian coordinates of the form

The **FKT algorithm**, named after Fisher, Kasteleyn, and Temperley, counts the number of perfect matchings in a planar graph in polynomial time. This same task is #P-complete for general graphs. Counting the number of matchings, even for planar graphs, is also #P-complete. The key idea is to convert the problem into a Pfaffian computation of a skew-symmetric matrix derived from a planar embedding of the graph. The Pfaffian of this matrix is then computed efficiently using standard determinant algorithms.

**Curtis Greene** is an American mathematician, specializing in algebraic combinatorics. He is the J. McLain King Professor of Mathematics at Haverford College in Pennsylvania.

- Thomas Zaslavsky at the Mathematics Genealogy Project
- Thomas Zaslavsky's homepage
- Microsoft academic search

The **Mathematics Genealogy Project** is a web-based database for the academic genealogy of mathematicians. By 13 February 2019, it contained information on 238,725 mathematical scientists who contributed to research-level mathematics. For a typical mathematician, the project entry includes graduation year, thesis title, *alma mater*, doctoral advisor, and doctoral students.

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