Presenting some of Stanley's (b. 1944) most influential papers, the editors find in them the recurring theme that innocent counting problems can reveal deep structure, connecting them to algebra, geometry, and topology. Among the topics are the theory and application of plane partitions, linear homogeneous Diophantine equations and magic labelings of graphs, two combinatorial applications of the Aleksandrov-Fenchel inequalities, on the number of reduced decompositions of elements of Coxeter groups, and a symmetric function generalization of the chromatic polynomial of a graph. The facsimile pages retain the original page numbers. Annotation ©2017 Ringgold, Inc., Portland, OR (protoview.com)
The early years
How the upper bound conjecture was proved
Theory and application of plane partitions: Part 1
Theory and application of plane partitions. Part 2
Modular elements of geometric lattices
Supersolvable lattices
Linear homogeneous diophantine equations and magic labelings of graphs
Acyclic orientations of graphs
Combinatorial reciprocity theorems
The upper bound conjecture and Cohen-Macaulay rings
Combinatorial reciprocity theorems
Binomial posets, Mobius inversion, and permutation enumeration
Eulerian partitions of a unit hypercube, voir note ci-apres
Hilbert functions of graded algebras
The number of faces of a simplicial convex polytope
Differential posets
Weyl groups, the hard Lefschetz theorem, and the Sperner property
Two combinatorial applications of the Aleksandrov-Fenchel inequalities
Linear diophantine equations and local cohomology
Some aspects of groups acting on finite posets
with A. Bjorner and A. Garsia, An introduction to Cohen-Macaulay partially
ordered sets
An introduction to combinatorial commutative algebra
On the number of reduced decompositions of elements of Coxeter groups
A baker's dozen of conjectures concerning plane partitions
Unimodality and Lie superalgebras
Two poset polytopes
Generalized $H$-vectors, intersection cohomology of toric varieties, and
related results
Differentiably finite power series
Log-concave and unimodal sequences in algebra, combinatorics, and geometry
Some combinatorial properties of Jack symmetric functions
Subdivisions and local $h$-vectors
with S. Billey and W. Jokusch, Some combinatorial properties of Schubert
polynomials
with S. Fomin, Schubert polynomials and the nilCoxeter algebra
Flag $f$-vectors and the $cd$-index
A symmetric function generalization of the chromatic polynomial of a graph
Irreducible symmetric group characters of rectangular shape
Increasing and decreasing subsequences and their variants
Promotion and evacuation
A conjectured combinatorial interpretation of the normalized irreducible
character values of the symmetric group.
Patricia Hersh, North Carolina State University, Raleigh, NC, USA.
Thomas Lam, University of Michigan, Ann Arbor, MI, USA.
Pavlo Pylyavskyy, University of Michigan, Ann Arbor, MI, USA.
Victor Reiner, University of Minnesota, Minneapolis, MN, USA.
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