Selected Works of Richard P. Stanley

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American Mathematical Soc., May 17, 2017 - Combinatorial analysis - 814 pages
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Richard Stanley's work in combinatorics revolutionized and reshaped the subject. Many of his hallmark ideas and techniques imported from other areas of mathematics have become mainstays in the framework of modern combinatorics. In addition to collecting several of Stanley's most influential papers, this volume also includes his own short reminiscences on his early years, and on his celebrated proof of The Upper Bound Theorem.

 

 

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Contents

Introduction
12
Enumeration of ColumnStrict Plane Partitions
33
Enumeration of Ordinary Plane Partitions
42
part 2
43
Conclusion
48
Supersolvable lattices
59
Linear homogeneous Diophantine equations and magic labelings of graphs
81
Acyclic orientations of graphs
107
On the number of reduced decompositions of elements of Coxeter groups
391
Unimodality and Lie superalgebras
415
Two poset polytopes
435
Generalized Hvectors intersection cohomology of toric varieties and related
451
Differential posets
479
Logconcave and unimodal sequences in algebra combinatorics
523
Some combinatorial properties of Jack symmetric functions
559
Subdivisions and local hvectors
603

The Upper Bound Conjecture and CohenMacaulay rings
175
Eulerian partitions of a unit hypercube
217
The number of faces of a simplicial convex polytope
247
Weyl groups the hard Lefschetz theorem and the Sperner property
265
Two combinatorial applications of the AleksandrovFenchel inequalities
283
Some aspects of groups acting on finite posets
313
An introduction to combinatorial commutative algebra
375
with Sara Billey and William Jockusch Some combinatorial properties
647
with Sergey Fomin Schubert polynomials and the nilCoxeter algebra
677
A symmetric function generalization of the chromatic polynomial of
707
Irreducible symmetric group characters of rectangular shape
737
Promotion and evacuation
785
A conjectured combinatorial interpretation of the normalized irreducible
809
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About the author (2017)

Edited by Patricia Hersh: North Carolina State University, Raleigh, NC,
Thomas Lam: University of Michigan, Ann Arbor, MI,
Pavlo Pylyavskyy: University of Minnesota, Minneapolis, MN,
Victor Reiner: University of Minnesota, Minneapolis, MN

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