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What Is Enumerative Combinatorics

- R. Stanley
- Mathematics
- 31 July 1986

The basic problem of enumerative combinatorics is that of counting the number of elements of a finite set. Usually are given an infinite class of finite sets S i where i ranges over some index set I… Expand

Combinatorics and commutative algebra

- R. Stanley
- Mathematics
- 1983

This text offers an overview of two of the main topics in the connections between commutative algebra and combinatorics. The first concerns the solutions of linear equations in non-negative integers.… Expand

Enumerative Combinatorics: Volume 1

- R. Stanley
- Mathematics
- 12 December 2011

Richard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition of… Expand

Hilbert functions of graded algebras

- R. Stanley
- Mathematics
- 1 April 1978

Let R be a Noetherian commutative ring with identity, graded by the nonnegative integers N. Thus the additive group of R has a direct-sum decomposition R = R, + R, + ..., where RiRi C R,+j and 1 E R,… Expand

A Symmetric Function Generalization of the Chromatic Polynomial of a Graph

- R. Stanley
- Mathematics
- 1 March 1995

Abstract For a finite graph G with d vertices we define a homogeneous symmetric function XG of degree d in the variables x1, x2, ... . If we set x1 = ... = xn= 1 and all other xi = 0, then we obtain… Expand

The number of faces of a simplicial convex polytope

- R. Stanley
- Mathematics
- 1 March 1980

Let P be a simplicial convex d-polytope with fi = fi(P) faces of dimension i. The vector f(P) = (f. , fi ,..., fdel) is called the f-vector of P. In 1971 McMullen [6; 7, p. 1791 conjectured that a… Expand

Some combinatorial properties of Jack symmetric functions

- R. Stanley
- Mathematics
- 1 September 1989

If 1, + L, + = n, then write 2+-n or 1% = n. If p is another partition, then write p c J. if pi 6 %, for all i (i.e., if the diagram of 1. contains the diagram of p), If IpL/ = Ii.1 then write p 2 1.… Expand

Two poset polytopes

- R. Stanley
- Mathematics, Computer Science
- Discret. Comput. Geom.
- 1 April 1986

TLDR

Log‐Concave and Unimodal Sequences in Algebra, Combinatorics, and Geometry a

- R. Stanley
- Mathematics
- 1 December 1989

A sequence a,, a,, . . . , a, of real numbers is said to be unimodal if for some 0 s j _c n we have a, 5 a , 5 . . 5 ai 2 a,,, 2 . . 2 a,, and is said to be logarithmically concave (or log-concave… Expand

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