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What Is Enumerative Combinatorics
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 IExpand
Combinatorics and commutative algebra
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
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 ofExpand
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
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 obtainExpand
The number of faces of a simplicial convex polytope
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 aExpand
Some combinatorial properties of Jack symmetric functions
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
A transfer map allows us to transfer properties of ϑ(P) to ℒ(P), and to transfer known inequalities involving linear extensions ofP to some new inequalities. Expand
Log‐Concave and Unimodal Sequences in Algebra, Combinatorics, and Geometry a
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-concaveExpand