"...a blend of erudition (fascinating and sometimes obscure historical minutiae abound), popularization (mathematical rigor is relegated to appendices) and exposition (the reader need have little knowledge of the fields involved) ...and the illustrations include many superb examples of computer graphics that are works of art in their own right." Nature

The Fractal Geometry of Nature

I. Symmetric functions II. Hall polynomials III. HallLittlewood symmetric functions IV. The characters of GLn over a finite field V. The Hecke ring of GLn over a finite field VI. Symmetric functions with two parameters VII. Zonal polynomials

Symmetric functions and Hall polynomials

/pdf/spatial-interaction-and-the-statistical-analysis-of-lattice-3zebq2vlhh.pdf

Spatial Interaction and the Statistical Analysis of Lattice Systems

What do a seventeenth-century mortality table (whose causes of death include "fainted in a bath," "frighted," and "itch"); the identification of South Africans during apartheid as European, Asian, colored, or black; and the separation of machine- from hand-washables have in common? All are examples of classification -- the scaffolding of information infrastructures. In Sorting Things Out, Geoffrey C. Bowker and Susan Leigh Star explore the role of categories and standards in shaping the modern world. In a clear and lively style, they investigate a variety of classification systems, including the International Classification of Diseases, the Nursing Interventions Classification, race classification under apartheid in South Africa, and the classification of viruses and of tuberculosis. The authors emphasize the role of invisibility in the process by which classification orders human interaction. They examine how categories are made and kept invisible, and how people can change this invisibility when necessary. They also explore systems of classification as part of the built information environment. Much as an urban historian would review highway permits and zoning decisions to tell a city's story, the authors review archives of classification design to understand how decisions have been made. Sorting Things Out has a moral agenda, for each standard and category valorizes some point of view and silences another. Standards and classifications produce advantage or suffering. Jobs are made and lost; some regions benefit at the expense of others. How these choices are made and how we think about that process are at the moral and political core of this work. The book is an important empirical source for understanding the building of information infrastructures.

https://www.reciis.icict.fiocruz.br/index.php/reciis/article/download/794/1436

Sorting Things Out: Classification and Its Consequences

1. Basic convexity 2. Boundary structure 3. Minkowski addition 4. Curvature measure and quermass integrals 5. Mixed volumes 6. Inequalities for mixed volumes 7. Selected applications Appendix.

/pdf/convex-bodies-the-brunn-minkowski-theory-3raynvod45.pdf

Convex bodies : the Brunn-Minkowski theory

On the foundations of combinatorial theory I. Theory of Möbius Functions

Ordinary Differential Equations

Introduction 1. The Buffon needle problem 2. Valuation and integral 3. A discrete lattice 4. The intrinsic volumes for parallelotopes 5. The lattice of polyconvex sets 6. Invariant measures on Grassmannians 7. The intrinsic volumes for polyconvex sets 8. A characterization theorem for volume 9. Hadwiger's characterization theorem 10. Kinematic formulas for polyconvex sets 11. Polyconvex sets in the sphere References Index of symbols Index.

http://www.gbv.de/dms/goettingen/234513152.pdf

Introduction to Geometric Probability

The following material is discussed in this paper: Incidence Coalgebras for PO sets; Reduced Boolean Coalgebras; Divided Powers Coalgebra; Dirichlet Coalgebra; Eulerian Coalgebra; Faa di Bruno Bialgebra; Incidence Coalgebras for Categories; The Umbral Calculus; Infinitesimal Coalgebras; Creation and Annihilation Operators; Point Lattice Coalgebras; Restricted Placements; Cleavages; and Hereditary Bialgebras.

Coalgebras and Bialgebras in Combinatorics

/pdf/baxter-algebras-and-combinatorial-identities-ii-jo9a9n68p5.pdf

Baxter algebras and combinatorial identities. II

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