Selected Works of Richard P. Stanley

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.

• The early yearsHow the upper bound conjecture was provedTheory and application of plane partitions: Part 1Theory and application of plane partitions. Part 2Modular elements of geometric latticesSupersolvable latticesLinear homogeneous diophantine equations and magic labelings of graphsAcyclic orientations of graphsCombinatorial reciprocity theoremsThe upper bound conjecture and Cohen-Macaulay ringsCombinatorial reciprocity theoremsBinomial posets, Mobius inversion, and permutation enumerationEulerian partitions of a unit hypercube, voir note ci-apresHilbert functions of graded algebrasThe number of faces of a simplicial convex polytopeDifferential posetsWeyl groups, the hard Lefschetz theorem, and the Sperner propertyTwo combinatorial applications of the Aleksandrov-Fenchel inequalitiesLinear diophantine equations and local cohomologySome aspects of groups acting on finite posetswith A. Bjorner and A. Garsia, An introduction to Cohen-Macaulay partially ordered setsAn introduction to combinatorial commutative algebraOn the number of reduced decompositions of elements of Coxeter groupsA baker's dozen of conjectures concerning plane partitionsUnimodality and Lie superalgebrasTwo poset polytopesGeneralized $H$-vectors, intersection cohomology of toric varieties, and related resultsDifferentiably finite power seriesLog-concave and unimodal sequences in algebra, combinatorics, and geometrySome combinatorial properties of Jack symmetric functionsSubdivisions and local $h$-vectorswith S. Billey and W. Jokusch, Some combinatorial properties of Schubert polynomialswith S. Fomin, Schubert polynomials and the nilCoxeter algebraFlag $f$-vectors and the $cd$-indexA symmetric function generalization of the chromatic polynomial of a graphIrreducible symmetric group characters of rectangular shapeIncreasing and decreasing subsequences and their variantsPromotion and evacuationA conjectured combinatorial interpretation of the normalized irreducible character values of the symmetric group.