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Einar Steingrímsson
Einar Steingrímsson (born 20 July 1955) is an Icelandic mathematician whose research lies in enumerative combinatorics, especially the study of permutation patterns and permutation statistics. He is a research professor (emeritus) in the School of Mathematics and Statistics at the University of Strathclyde. Early life and education Einar grew up in Reykjavík and left secondary school early at age eighteen (the normal graduation age at the time was twenty), and trained as a ship builder at Slippstöðin in Akureyri. After completing qualifying examinations independently, he enrolled at the University of Pennsylvania. He graduated there as a BA and MA in mathematics in 1987, and as PhD at the Massachusetts Institute of Technology in 1992 under the supervision of Richard P. Stanley; his dissertation was titled ''Permutation Statistics of Indexed and Poset Permutations''. Career Einar moved to Gothenburg, Sweden in 1990, while still a graduate student at the Massachusetts Institut ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorics
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to 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. Combinatorics is well known for the breadth of the problems it tackles. Combinatorial problems arise in many areas of pure mathematics, notably in algebra, probability theory, topology, and geometry, as well as in its many application areas. Many combinatorial questions have historically been considered in isolation, giving an ''ad hoc'' solution to a problem arising in some mathematical context. In the later twentieth century, however, powerful and general theoretical methods were developed, making combinatorics into an independent branch of mathematics in its own right. One of the oldest and most accessible parts of combinatorics ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Permutation Statistics
The statistics of random permutations, such as the cycle structure of a random permutation are of fundamental importance in the analysis of algorithms, especially of sorting algorithms, which operate on random permutations. Suppose, for example, that we are using quickselect (a cousin of quicksort) to select a random element of a random permutation. Quickselect will perform a partial sort on the array, as it partitions the array according to the pivot. Hence a permutation will be less disordered after quickselect has been performed. The amount of disorder that remains may be analysed with generating functions. These generating functions depend in a fundamental way on the generating functions of random permutation statistics. Hence it is of vital importance to compute these generating functions. The article on random permutations contains an introduction to random permutations. The fundamental relation Permutations are sets of labelled cycles. Using the labelled case of the Fla ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
People From Reykjavík
The term "the people" refers to the public or common mass of people of a polity. As such it is a concept of human rights law, international law as well as constitutional law, particularly used for claims of popular sovereignty. In contrast, a people is any plurality of persons considered as a whole. Used in politics and law, the term "a people" refers to the collective or community of an ethnic group or nation. Concepts Legal Chapter One, Article One of the Charter of the United Nations states that "peoples" have the right to self-determination. Though the mere status as peoples and the right to self-determination, as for example in the case of Indigenous peoples (''peoples'', as in all groups of indigenous people, not merely all indigenous persons as in ''indigenous people''), does not automatically provide for independent sovereignty and therefore secession. Indeed, judge Ivor Jennings identified the inherent problems in the right of "peoples" to self-determination, as i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Living People
Purpose: Because living persons may suffer personal harm from inappropriate information, we should watch their articles carefully. By adding an article to this category, it marks them with a notice about sources whenever someone tries to edit them, to remind them of WP:BLP (biographies of living persons) policy that these articles must maintain a neutral point of view, maintain factual accuracy, and be properly sourced. Recent changes to these articles are listed on Special:RecentChangesLinked/Living people. Organization: This category should not be sub-categorized. Entries are generally sorted by family name In many societies, a surname, family name, or last name is the mostly hereditary portion of one's personal name that indicates one's family. It is typically combined with a given name to form the full name of a person, although several give .... Maintenance: Individuals of advanced age (over 90), for whom there has been no new documentation in the last ten ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1955 Births
Events January * January 3 – José Ramón Guizado becomes president of Panama. * January 17 – , the first Nuclear marine propulsion, nuclear-powered submarine, puts to sea for the first time, from Groton, Connecticut. * January 18–January 20, 20 – Battle of Yijiangshan Islands: The Chinese Communist People's Liberation Army seizes the islands from the Republic of China (Taiwan). * January 22 – In the United States, The Pentagon announces a plan to develop intercontinental ballistic missiles (ICBMs), armed with nuclear weapons. * January 23 – The Sutton Coldfield rail crash kills 17, near Birmingham, England. * January 25 – The Presidium of the Supreme Soviet of the Soviet Union announces the end of the war between the USSR and Germany, which began during World War II in 1941. * January 28 – The United States Congress authorizes President Dwight D. Eisenhower to use force to protect Taiwan from the People's Republic of China. February * February 10 – T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stanley–Wilf Conjecture
The Stanley–Wilf conjecture, formulated independently by Richard P. Stanley and Herbert Wilf in the late 1980s, states that the growth rate of every proper permutation class is Exponential growth, singly exponential. It was proved by and is no longer a conjecture. Marcus and Tardos actually proved a different conjecture, due to , which had been shown to imply the Stanley–Wilf conjecture by . Statement The Stanley–Wilf conjecture states that for every permutation ''β'', there is a constant ''C'' such that the number , ''S''''n''(''β''), of permutations of length ''n'' which avoid ''β'' as a permutation pattern is at most ''C''''n''. As observed, this is equivalent to the convergence of the Limit (mathematics), limit :\lim_ \sqrt[n]. The upper bound given by Marcus and Tardos for ''C'' is Exponential function, exponential in the length of ''β''. A stronger conjecture of had stated that one could take ''C'' to be , where ''k'' denotes the length of ''β'', but this con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lauren Williams (mathematician)
Lauren Kiyomi Williams (born 1978) is an American mathematician known for her work on cluster algebras, tropical geometry, algebraic combinatorics, amplituhedra, and the positive Grassmannian. She is Dwight Parker Robinson Professor of Mathematics at Harvard University.. Education Williams's father is an engineer; her mother is third-generation Japanese American. She grew up in Los Angeles, where her interest in mathematics was sparked by winning a fourth-grade mathematics contest. She was the valedictorian of Palos Verdes Peninsula High School in 1996, and while there participated in summer research at the Massachusetts Institute of Technology with Satomi Okazaki, a student of her eventual advisor, Richard P. Stanley. She graduated magna cum laude from Harvard University in 2000 with a A.B. in mathematics, and received her PhD in 2005 at the Massachusetts Institute of Technology under the supervision of Stanley. Her dissertation was titled ''Combinatorial Aspects of Total Pos ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Gothenburg
The University of Gothenburg () is a List of universities in Sweden, university in Sweden's second largest city, Gothenburg. Founded in 1891, the university is the third-oldest of the current List of universities in Sweden#Public universities, Swedish universities and, with 53,624 students and 6,707 staff members, it is one of the largest universities in the Nordic countries. About With its eight faculties and 38 departments, the University of Gothenburg is one of the most wide-ranging and versatile universities in Sweden. Its eight faculties offer training in the Creative Arts, Social Sciences, Natural Sciences, Humanities, Education, Information Technology, Business, Economics and Law, and Health Sciences. The University of Gothenburg has the highest number of applicants per study place in many of its subjects and courses, making it one of the most popular universities in Sweden. History The University of Gothenburg was founded as ''Göteborgs högskola'' (Gothenburg Uni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gothenburg
Gothenburg ( ; ) is the List of urban areas in Sweden by population, second-largest city in Sweden, after the capital Stockholm, and the fifth-largest in the Nordic countries. Situated by the Kattegat on the west coast of Sweden, it is the gubernatorial seat of Västra Götaland County, with a population of approximately 600,000 in the city proper and about 1.1 million inhabitants in Metropolitan Gothenburg, the metropolitan area. Gustavus Adolphus, King Gustavus Adolphus founded Gothenburg by royal charter in 1621 as a heavily fortified, primarily Dutch, trading colony. In addition to the generous privileges given to his Dutch allies during the ongoing Thirty Years' War, e.g. tax relaxation, he also attracted significant numbers of his German and Scottish allies to populate his only town on the western coast; this trading status was furthered by the founding of the Swedish East India Company. At a key strategic location at the mouth of the , where Scandinavia's largest dr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Akureyri
Akureyri (, ) is a town in northern Iceland, the country's fifth most populous Municipalities of Iceland, municipality (under the official name of Akureyrarbær , 'town of Akureyri') and the largest outside the Capital Region (Iceland), Capital Region. The municipality includes the town's neighbourhood at the head of Eyjafjörður and two farther islands: Hrísey at the mouth of Eyjafjörður and Grímsey off the coast. Nicknamed the "Capital of North Iceland", Akureyri is an important port and fishing centre. The area where Akureyri is located was settled in the 9th century, but did not receive a municipal charter until 1786. Allies of World War II, Allied units were based in the town during World War II. Further growth occurred after the war as the Icelandic population increasingly moved to urban areas. The area has a relatively mild climate because of geographical factors, and the town's ice-free harbour has played a significant role in its history. History The Norsemen, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Permutation Pattern
In combinatorial mathematics and theoretical computer science, a (classical) permutation pattern is a sub-permutation of a longer permutation. Any permutation may be written in one-line notation as a sequence of entries representing the result of applying the permutation to the sequence 123...; for instance the sequence 213 represents the permutation on three elements that swaps elements 1 and 2. If π and σ are two permutations represented in this way (these variable names are standard for permutations and are unrelated to the number pi), then π is said to ''contain'' σ as a ''pattern'' if some subsequence of the entries of π has the same relative order as all of the entries of σ. For instance, permutation π contains the pattern 213 whenever π has three entries ''x'', ''y'', and ''z'' that appear within π in the order ''x''...''y''...''z'' but whose values are ordered as ''y'' < ''x'' < ''z'', the same as the ordering of the values in the permutation 2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Pennsylvania
The University of Pennsylvania (Penn or UPenn) is a Private university, private Ivy League research university in Philadelphia, Pennsylvania, United States. One of nine colonial colleges, it was chartered in 1755 through the efforts of founder and first president Benjamin Franklin, who had advocated for an educational institution that trained leaders in academia, commerce, and public service. The university has four undergraduate schools and 12 graduate and professional schools. Schools enrolling undergraduates include the College of Arts and Sciences, the University of Pennsylvania School of Engineering and Applied Science, School of Engineering and Applied Science, the Wharton School, and the University of Pennsylvania School of Nursing, School of Nursing. Among its graduate schools are its University of Pennsylvania Law School, law school, whose first professor, James Wilson (Founding Father), James Wilson, helped write the Constitution of the United States, U.S. Cons ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
