Selected Works of Richard P. StanleyRichard 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
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 
Common terms and phrases
acyclic algebra bijection coefficients CohenMacaulay rings columnstrict plane partitions compute conjecture convex polytope Corollary correspondence decomposition define definition degree denote the number dimension distributive lattice easily seen Ehrhart elements equal equations equivalent Eulerian poset Example faces finite finitelygenerated Galgebra given Gorenstein graded graph Hence Hilbert function homogeneous induction integers irreducible isomorphic lattice cones Lemma length Let G LHDsystem linear transformation logconcave magic labelings Mathematics matrix maximal chain Mobius function modular module monoid monomials Moreover multiplicity Nsolutions nonnegative integers nonzero notation obtain order ideal Precursive partially ordered set permutation plane partitions polynomial positive integers power series Proc proof follows Proposition prove rdifferential poset Rproperty R. P. Stanley rank rational functions reciprocity theorem representation result satisfying Schur functions sequence simplicial complex solution SSlattice subdivision subset Suppose symmetric functions symmetric group Theorem 3.1 triangulation unimodal unique variables vector space vertex vertices