Gian-Carlo Rota, the Man / Part I: |
Gianco, my Brother / Ester Gasperoni Rota1: |
References |
Remembering Gian-Carlo Rota / Joseph J. Kohn2: |
Gian-Carlo Rota, the Mathematician / Part II: |
A Glimpse of Vector Invariant Theory. The Points of View of Weyl, Rota, De Concini and Procesi, and Grosshans / Andrea Brini3: |
Introduction / 3.1: |
The Characteristic Zero Approach / 3.2: |
Preliminaries / 3.2.1: |
Weyl's Theorem (The Reduction Principle) / 3.2.2: |
Absolute Invariants for the Special Linear Group S L(d) / 3.2.3: |
Absolute Invariants for the Symplectic Group S p2m / 3.2.4: |
Absolute Invariants for the Special Orthogonal Group S O(d) / 3.2.5: |
Absolute Invariants for the Orthogonal Group O(d) / 3.2.6: |
The Straightening Formulae / 3.3: |
Standard Young Tableaux / 3.3.1: |
Bideterminants / 3.3.2: |
Pfaffians / 3.3.3: |
Gramians / 3.3.4: |
The E. Pascal Theorems and the Cancellation Laws / 3.4: |
The E. Pascal Theorem and the Cancellation Law for Scalar Products / 3.4.1: |
The E. Pascal Theorem and the Cancellation Law for Symplectic Products / 3.4.2: |
The E. Pascal Theorem and the Cancellation Law for Inner Products / 3.4.3: |
The First and the Second Fundamental Theorems / 3.5: |
The First Fundamental Theorems / 3.5.1: |
The Second Fundamental Theorems / 3.5.2: |
Grosshans's Theorem / 3.6: |
Partitions of a Finite Partially Ordered Set / Pietro Codara4: |
Background, and Preliminary Results / 4.1: |
Partitions as Sets of Fibres / 4.3: |
Partitions as Partially Ordered Sets of Blocks / 4.4: |
Partitions Induced by Quasiorders / 4.5: |
Further Work / 4.6: |
An Algebra of Pieces of Space - Hermann Grassmann to Gian Carlo Rota / Henry Crapo5: |
Almost Ten Years Later / 5.1: |
Synthetic Projective Geometry / 5.2: |
Hermann Grassmann's Algebra / 5.3: |
Extensors and Vectors / 5.4: |
Reduced Forms / 5.5: |
Grassmann-Cayley Algebra, Peano Spaces / 5.6: |
Whitney Algebra / 5.7: |
Geometric Product / 5.8: |
Regressive Product / 5.9: |
Higher Order Syzygies / 5.10: |
Balls in Boxes / 5.11: |
The Eleventh and Twelveth Problems of Rota's Fubini Lectures: from Cumulants to Free Probability Theory / Elvira Di Nardo ; Domenico Senato6: |
Prologue / 6.1: |
The Classical Umbral Calculus / 6.2: |
Generating Functions / 6.2.1: |
Sequences of Binomial Type, Bell Umbrae and Poisson Processes / 6.3: |
Cumulants / 6.4: |
Singleton Umbra / 6.4.1: |
Cumulant Umbra / 6.4.2: |
Applications in Statistics / 6.5: |
U-Statistics / 6.5.1: |
Moments of Sampling Distributions / 6.5.2: |
Products of Statistics / 6.5.3: |
k-statistics / 6.5.4: |
Fast Symbolic Computation of k-statistics / 6.5.5: |
Sheppard's Corrections / 6.5.6: |
Sheffer Sequences / 6.6: |
Abel Polynomials / 6.6.1: |
Quasi-free Cumulant Umbra / 6.6.2: |
Boolean Cumulants / 6.6.3: |
Free Cumulant Theory / 6.7: |
Two Examples of Applied Universal Algebra / Joseph P. S. Kung7: |
The Bohnenblust-Spitzer Identity / 7.1: |
Baxter Algebras / 7.3: |
The Standard Baxter Algebra / 7.4: |
A Precursor Identity / 7.5: |
Abstract Random Variables / 7.6: |
On the Euler Characteristic of Finite Distributive Lattices / Emanuele Munarini8: |
Posets and Distributive Lattices / 8.1: |
Euler Characteristic / 8.3: |
Uniform Distributions of the Characteristic / 8.4: |
X-uniform Lattices / 8.4.1: |
Order-preserving Euler Characteristic / 8.4.2: |
Rank X-uniform Lattices / 8.4.3: |
Pseudo-planar Distributive Lattices / 8.5: |
Graphs and Hypergraphs / 8.6: |
Dual Gödel Lattices / 8.7: |
Tree maps / 8.8: |
Rota, Probability, Algebra and Logic / Daniele Mundici9: |
MV-algebraic States and De Finetti Coherence Criterion / 9.1: |
MV-algebraic and C*-algebraic States After Elliott Classification / 9.2: |
MV-algebraic ?-states and Carathéodory Probability Theory / 9.3: |
A Symbolic Treatment of Abel Polynomials / Pasquale Petrullo10: |
Abel polynomials, Lagrange inversion formula and sequences of binomial type / 10.1: |
Generalized Abel polynomials / 10.3: |
Cumulants and convolutions / 10.4: |
Gian-Carlo Rota, the Philosopher / Part III: |
Ethics in Thought. Gian-Carlo Rota and Philosophy / Francesca Bonicalzi11: |
Telling/Inventing the Truth / 11.1: |
The Winding Streets, and the Straight and Wide Avenue of Precision / 11.2: |
The Food of Philosophical Thought and the Medicine of Axiomatics / 11.3: |
The Ethics of Knowledge and the Genesis of its Disciplines / 11.4: |
Indiscrete Variations on Gian-Carlo Rota's Themes / Carlo Cellucci12: |
The Existence of Mathematical Objects / 12.1: |
Irrelevance of the Existence of Mathematical Objects / 12.2.1: |
Mathematical Objects as Hypotheses / 12.2.2: |
Hypotheses vs. Fictions / 12.2.3: |
Existence and Identity / 12.2.4: |
The Inexhaustibility of Mathematical Objects / 12.2.5: |
Definition in Mathematics / 12.3: |
Definition, Description and Analysis of Concepts / 12.3.1: |
Definition in Mathematics and in Philosophy / 12.3.2: |
The Alleged Circularity of Definitions and Theorems / 12.3.3: |
The Notion of Proof / 12.4: |
Proof as the Opening up of Possibilities / 12.4.1: |
Axiomatic Presentation and Gödel's Incompleteness Theorems / 12.4.2: |
Are there Definitive Proofs? / 12.4.3: |
Proof and Evidence / 12.4.4: |
The Relation of Philosophy of Mathematics to Mathematics / 12.5: |
The Descriptive Character of the Philosophy of Mathematics / 12.5.1: |
The Need for a Drastic Overhaul of Logic / 12.5.2: |
Rota's Place in the Philosophy of Mathematics / 12.6: |
On the Courage Needed to Do Phenomenology. Rota and Analytic Philosophy / Albino Lanciani ; Claudio Majolino13: |
Twilight of an Idol / 13.1: |
Three Senses of Phenomenology / 13.2: |
Coda / 13.3: |
Rota's Philosophical Insights / Massimo Mugnai14: |
What Kind of Reductionism? / 14.1: |
Rota's Objectivism and Husserl's Naturalism / 14.3: |
Beyond Classical Logic / 14.4: |
Concluding Remarks / 14.5: |
"A Minority View". Gian-Carlo Rota's Phenomenological Realism / Fabrizio Palombi15: |
Considerations on the Problem of Realism / 15.1: |
Phenomenological Realism / 15.2: |
Fringe Phenomena and State-of-Mind / 15.3: |
Psychologistic Misunderstandings / 15.4: |
Descriptions, Not Prescriptions / 15.5: |
Gian-Carlo Rota, the Man / Part I: |
Gianco, my Brother / Ester Gasperoni Rota1: |
References |