This monograph provides a self-contained introduction to symmetric functions and their use in enumerative combinatorics. It is the first book to explore many of the methods and results that the authors present. Numerous exercises are included throughout, along with full solutions, to illustrate concepts and also highlight many interesting mathematical ideas. The text begins by introducing fundamental combinatorial objects such as permutations and integer partitions, as well as generating functions. Symmetric functions are considered in the next chapter, with a unique emphasis on the combinatorics of the transition matrices between bases of symmetric functions. Chapter 3 uses this introductory material to describe how to find an assortment of generating functions for permutation statistics, and then these techniques are extended to find generating functions for a variety of objects in Chapter 4. The next two chapters present the Robinson-Schensted-Knuth algorithm and a method for proving Pólya’s enumeration theorem using symmetric functions. Chapters 7 and 8 are more specialized than the preceding ones, covering consecutive pattern matches in permutations, words, cycles, and alternating permutations and introducing the reciprocity method as a way to define ring homomorphisms with desirable properties. Counting with Symmetric Functions will appeal to graduate students and researchers in mathematics or related subjects who are interested in counting methods, generating functions, or symmetric functions. The unique approach taken and results and exercises explored by the authors make it an important contribution to the mathematical literature.
CIA agent Jordan Sandor's mission is more complex and has more at stake than any he has faced before. From Bermuda to the United Kingdom, from France to the deserts of Iraq, Jordan must face down villains both known and unknown, recognized and hidden, as he struggles to prevent the deaths of tens of thousands of innocent people. Needing help as never before, Sandor calls upon his usual group of talented associates, as well as top CIA analyst Beth Sharrow, a former lover still willing to risk her life and career to help Sandor.
Laparoscopic Colorectal Surgery provides an authoritative, team-oriented approach to the latest state-of-the-art laparoscopic colorectal procedures and surgical techniques. Written by pioneers in the field, this text will supply surgeons with all the information necessary to accomplish advanced laparoscopic procedures. Comprehensive discussions of positioning, instrumentation, cannulas, surgical techniques, special considerations, and considerations in cancer surgery are featured for a wide variety of major operative procedures, including - smallbowel resection - abdominoperineal resection - ileocolectomy, right colectomy, and total abdominal colectomy - proctosigmoidectomy - stoma construction and closure using laparoscopic techniques.
Comprehensive and complete, Shackelford’s Surgery of the Alimentary Tract delivers the definitive, clinically oriented, cutting-edge guidance you need to achieve optimal outcomes managing the entire spectrum of gastrointestinal disorders. Make effective use of the latest endoscopic, robotic, and minimally invasive procedures as well as medical therapies with unbeatable advice from a "who’s who" of international authorities! Find expert answers to any clinical question in gastrointestinal surgery, from the esophagus to the colon. See exactly what to look for and how to proceed from an abundance of beautifully detailed intraoperative and laparoscopic photographs.
Polycystic Ovary Syndrome discusses the use of animal models in the study of PCOS the occurrence of ovarian and adrenal abnormalities, cardiovascular risks, abnormal insulin secretion, and endothelial dysfunction in PCOS modern therapeutic modalities, such as manipulation of diet and lifestyle, metabolic phenotyping
This is the first study in half a century to focus on the election of 1796. At first glance, the first presidential contest looks unfamiliar—parties were frowned upon, there was no national vote, and the candidates did not even participate (the political mores of the day forbade it). Yet for all that, Jeffrey L. Pasley contends, the election of 1796 was “absolutely seminal,” setting the stage for all of American politics to follow. Challenging much of the conventional understanding of this election, Pasley argues that Federalist and Democratic-Republican were deeply meaningful categories for politicians and citizens of the 1790s, even if the names could be inconsistent and the institutional presence lacking. He treats the 1796 election as a rough draft of the democratic presidential campaigns that came later rather than as the personal squabble depicted by other historians. It set the geographic pattern of New England competing with the South at the two extremes of American politics, and it established the basic ideological dynamic of a liberal, rights-spreading American left arrayed against a conservative, society-protecting right, each with its own competing model of leadership. Rather than the inner thoughts and personal lives of the Founders, covered in so many other volumes, Pasley focuses on images of Adams and Jefferson created by supporters-and detractors-through the press, capturing the way that ordinary citizens in 1796 would have actually experienced candidates they never heard speak. Newspaper editors, minor officials, now forgotten congressman, and individual elector candidates all take a leading role in the story to show how politics of the day actually worked. Pasley's cogent study rescues the election of 1796 from the shadow of 1800 and invites us to rethink how we view that campaign and the origins of American politics.
Perspicuity is part of proof. If the process by means of which I get a result were not surveyable, I might indeed make a note that this number is what comes out - but what fact is this supposed to confirm for me? I don't know 'what is supposed to come out' . . . . 1 -L. Wittgenstein A feasible computation uses small resources on an abstract computa tion device, such as a 'lUring machine or boolean circuit. Feasible math ematics concerns the study of feasible computations, using combinatorics and logic, as well as the study of feasibly presented mathematical structures such as groups, algebras, and so on. This volume contains contributions to feasible mathematics in three areas: computational complexity theory, proof theory and algebra, with substantial overlap between different fields. In computational complexity theory, the polynomial time hierarchy is characterized without the introduction of runtime bounds by the closure of certain initial functions under safe composition, predicative recursion on notation, and unbounded minimization (S. Bellantoni); an alternative way of looking at NP problems is introduced which focuses on which pa rameters of the problem are the cause of its computational complexity and completeness, density and separation/collapse results are given for a struc ture theory for parametrized problems (R. Downey and M. Fellows); new characterizations of PTIME and LINEAR SPACE are given using predicative recurrence over all finite tiers of certain stratified free algebras (D.
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