Bruce Eli Sagan (born March 29, 1954) is an American Professor of Mathematics at Michigan State University. He specializes in enumerative, algebraic, and topological combinatorics. He is also known as a musician, playing music from Scandinavia and the Balkans.
Sagan is the son of Eugene Benjamin Sagan and Arlene Kaufmann Sagan. He grew up in Berkeley, California. He started playing classical violin at a young age under the influence of his mother who was a music teacher and conductor. He received his B.S. in mathematics (1974) from California State University, East Bay (then called California State University, Hayward). He received his Ph.D. in mathematics (1979) from the Massachusetts Institute of Technology. His doctoral thesis "Partially Ordered Sets with Hooklengths – an Algorithmic Approach" was supervised by Richard P. Stanley. [1] He was Stanley's third doctoral student. During his graduate school years he also joined and became music director of the Mandala Folkdance Ensemble.
Sagan held postdoctoral positions at Université Louis Pasteur (1979–1980), the University of Michigan (1980–1983), University College of Wales, Aberystwyth, Middlebury College (1984–1985), the University of Pennsylvania, and Université du Québec à Montréal (Fall, 1985), before becoming a faculty member at MSU in the Spring of 1986. He has held visiting positions at the Institute for Mathematics and its Applications (Spring, 1988), UCSD (Spring, 1991), the Royal Institute of Technology (1993–1994), MSRI (Winter, 1997), the Isaac Newton Institute (Winter, 2001), Mittag-Leffler Institute (Spring, 2005), and DIMACS (2005–2006). He was also a rotating Program Officer at the National Science Foundation (2007–2010). [2]
Sagan has published over 100 research papers. He has given over 300 talks in North America, Europe, Asia, and Australia. These have included keynote addresses at the Conference on Formal Power Series and Algebraic Combinatorics (2006) and the British Combinatorial Conference (2011). He has graduated 15 Ph.D. students. [1] During his time at Michigan State University, he has won two awards for teaching excellence. [3]
Sagan has been an Editor-in-Chief for the Electronic Journal of Combinatorics since 2004. [4]
Sagan plays music from the Scandinavian countries and the Balkans on fiddle and native instruments. These include the Swedish nyckelharpa, the Norwegian hardingfele, and the Bulgarian gadulka. In 1985 he and his then wife, Judy Barlas, founded the music and dance camp Scandinavian Week at Buffalo Gap (now known as Nordic Fiddles and Feet). He is currently a regular staff member at Northern Week at Ashokan run by Jay Ungar and Molly Mason. In 1994 he was awarded the Zorn Medal in Bronze for his playing in front of a jury of Swedish musicians. He has performed and given workshops in North America, Europe, and Australia. He plays Swedish music as a duo with Brad Battey and also with Lydia Ievens. His trio Veselba, with Nan Nelson and Chris Rietz, performs music from Bulgaria. [5] [6]
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 and from evolutionary biology to computer science.
A fiddle is a bowed string musical instrument, most often a violin. It is a colloquial term for the violin, used by players in all genres, including classical music. Although in many cases violins and fiddles are essentially synonymous, the style of the music played may determine specific construction differences between fiddles and classical violins. For example, fiddles may optionally be set up with a bridge with a flatter arch to reduce the range of bow-arm motion needed for techniques such as the double shuffle, a form of bariolage involving rapid alternation between pairs of adjacent strings. To produce a "brighter" tone than the deep tones of gut or synthetic core strings, fiddlers often use steel strings. The fiddle is part of many traditional (folk) styles, which are typically aural traditions—taught "by ear" rather than via written music.
The polska is a family of music and dance forms shared by the Nordic countries: called polsk in Denmark, polka or polska in Estonia, polska in Sweden and Finland, and by several different names in Norway. Norwegian variants include pols, rundom, springleik, and springar. The polska is almost always seen as a partner dance in, although variants in 2
4 time, as well as in compound meters also exist.
A Hardanger fiddle is a traditional stringed instrument considered to be the national instrument of Norway. In modern designs, this type of fiddle is very similar to the violin, though with eight or nine strings and thinner wood. The earliest known example of the hardingfele is from 1651, made by Ole Jonsen Jaastad in Hardanger, Norway. Originally, the instrument had a rounder, narrower body. Around the year 1850, the modern layout with a body much like the violin became the norm.
Richard Peter Stanley is an Emeritus Professor of Mathematics at the Massachusetts Institute of Technology, in Cambridge, Massachusetts. From 2000 to 2010, he was the Norman Levinson Professor of Applied Mathematics. He received his Ph.D. at Harvard University in 1971 under the supervision of Gian-Carlo Rota. He is an expert in the field of combinatorics and its applications to other mathematical disciplines.
Traditional Nordic dance music is a type of traditional music or folk music that once was common in the mainland part of the Nordic countries — Scandinavia plus Finland. The person who plays this kind of music might be called speleman (Swedish/Norwegian), spelman (Swedish), spel(l)emann (Norwegian), pelimanni (Finnish) or spillemand (Danish). Finnish traditional dance music is often called pelimanni music in English, while there does not seem to exist a similar, widespread term for the corresponding music from the other countries. It is often more meaningful to distinguish between the traditional dance music from different regions than between music from the countries as such. Some concepts in the field can be defined as Norwegian or Finnish, but most are either common to all four countries or local. Besides the dance music tradition, all countries also have other traditions of folk music that are not shared to a similar extent.
Annbjørg Lien is a Norwegian musician, playing the hardingfele, violin, and nyckelharpa.
Hans Heinrich Wilhelm Magnus known as Wilhelm Magnus was a German-American mathematician. He made important contributions in combinatorial group theory, Lie algebras, mathematical physics, elliptic functions, and the study of tessellations.
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 algebra.
The mathematical field of combinatorics was studied to varying degrees in numerous ancient societies. Its study in Europe dates to the work of Leonardo Fibonacci in the 13th century AD, which introduced Arabian and Indian ideas to the continent. It has continued to be studied in the modern era.
The Byzantine lyra or lira was a medieval bowed string musical instrument in the Byzantine Empire. In its popular form, the lyra was a pear-shaped instrument with three to five strings, held upright and played by stopping the strings from the side with the fingertips and fingernails. The oldest known depiction of the instrument is on a Byzantine ivory casket, dated to circa 900–1100 AD, preserved in the Bargello in Florence. Modern variants of the lyra are still played throughout the Balkans and in areas surrounding the Black Sea, including Greece, Crete, Karpathos, Albania, Montenegro, Serbia, Bulgaria, North Macedonia, Croatia, Italy, Turkey and Armenia.
The Electronic Journal of Combinatorics is a peer-reviewed open access scientific journal covering research in combinatorial mathematics. The journal was established in 1994 by Herbert Wilf and Neil Calkin. The Electronic Journal of Combinatorics is a founding member of the Free Journal Network. According to the Journal Citation Reports, the journal had a 2017 impact factor of 0.762.
In mathematics, the Kostka number is a non-negative integer that is equal to the number of semistandard Young tableaux of shape and weight . They were introduced by the mathematician Carl Kostka in his study of symmetric functions.
In the study of permutation patterns, there has been considerable interest in enumerating specific permutation classes, especially those with relatively few basis elements. This area of study has turned up unexpected instances of Wilf equivalence, where two seemingly-unrelated permutation classes have the same numbers of permutations of each length.
Jon Hal Folkman was an American mathematician, a student of John Milnor, and a researcher at the RAND Corporation.
In algebra and in particular in algebraic combinatorics, a quasisymmetric function is any element in the ring of quasisymmetric functions which is in turn a subring of the formal power series ring with a countable number of variables. This ring generalizes the ring of symmetric functions. This ring can be realized as a specific limit of the rings of quasisymmetric polynomials in n variables, as n goes to infinity. This ring serves as universal structure in which relations between quasisymmetric polynomials can be expressed in a way independent of the number n of variables.
John Stembridge is a Professor of Mathematics at University of Michigan. He received his Ph.D. from Massachusetts Institute of Technology in 1985 under the direction of Richard P. Stanley. His dissertation was called Combinatorial Decompositions of Characters of SL(n,C).
Richard Alejandro Arratia is a mathematician noted for his work in combinatorics and probability theory.
Henry Howland Crapo 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.
In mathematics, the Young subgroups of the symmetric group are special subgroups that arise in combinatorics and representation theory. When is viewed as the group of permutations of the set , and if is an integer partition of , then the Young subgroup indexed by is defined by
