Let G be a finite graph with no loops (edges from a vertex to itself) or multiple edges. In [32] we defined a symmetric function XG = XG (x 1; x 2; : ::) which generalizes the chromatic polynomial G (n) of G. In this paper we will report on further work related to this symmetric function. We first review the definition of XG. We will denote by V = fv 1; : : : ; v d g the vertex set and by E the edge set of G. A coloring of G is any function : V! P = f1; 2; : ::g. If is a coloring, then set x Y
|
323
|
Symmetric Functions and Hall Polynomials
– Macdonald
- 1995
|
|
302
|
Enumerative Combinatorics
– Stanley
- 1999
|
|
184
|
Combinatorial Problems and Exercises
– Lovász
- 1993
|
|
102
|
Algebraic Combinatorics
– Godsil
- 1993
|
|
88
|
Hyperbolic groups, Essays in group theory
– Gromov
- 1987
|
|
65
|
The symmetric group
– Sagan
- 2001
|
|
63
|
Buildings of Spherical Type and Finite BN-pairs
– Tits
- 1974
|
|
55
|
Combinatorics and Commutative Algebra
– Stanley
- 1983
|
|
50
|
Linear decision trees: volume estimates and topological bounds
– Bjorner, Lov'asz, et al.
- 1992
|
|
48
|
The Tutte polynomial and its applications
– Brylawski, Oxley
|
|
47
|
Theory of monomer-dimer systems
– Heilmann, Lieb
- 1972
|
|
42
|
Heaps of pieces I: Basic definitions and combinatorial lemmas
– Viennot
- 1986
|
|
39
|
Linear Decision Trees, Subspace Arrangements and Mobius Functions
– Bjorner, Lov'asz
- 1994
|
|
39
|
log-concave and Polya frequency sequences in combinatorics
– Brenti, Unimodal
- 1989
|
|
34
|
Two Notes on Notation
– Knuth
|
|
33
|
symmetric function generalization of the chromatic polynomial of a graph
– Stanley, “A
- 1995
|
|
29
|
Subspace arrangements
– Bjorner
- 1992
|
|
24
|
Generating Functions
– Stanley
- 1978
|
|
21
|
The homology representations of the k-equal partition lattice
– Sundaram, Wachs
- 1994
|
|
19
|
A multiindexed Sturm sequence of polynomials and unimodality of certain combinatorial sequences
– Simion
- 1984
|
|
18
|
The homology of "k-equal" manifolds and related partition lattices
– Bjorner, Welker
- 1995
|
|
18
|
On immananants of Jacobi–Trudi matrices and permutations with restricted position
– Stanley, Stembridge
- 1990
|
|
15
|
On generating functions of totally positive sequences
– Aissen, Schoenberg, et al.
- 1952
|
|
15
|
The path-cycle symmetric function of a digraph
– Chow
- 1996
|
|
13
|
Incomparability graphs of (3 + 1)-free posets are s-positive,” Discrete Math
– Gasharov
- 1996
|
|
13
|
Clique polynomials and independent set polynomials of graphs
– Hoede, Li
- 1994
|
|
10
|
Dependence polynomials
– Fisher, Solow
- 1990
|
|
6
|
Totally positive matrices, Linear Algebra and Its Applications 90
– Ando
- 1987
|
|
6
|
On the numbers of independent k-sets in a claw free graph
– Hamidoune
- 1990
|
|
5
|
Interval Graphs and Interval Orders
– Fishburn
- 1985
|
|
4
|
Enumeration of Convex Polyominoes. A Generalization of the Robinson-Schensted
– Magid
- 1992
|
|
3
|
Problems on chain partitions
– Griggs
- 1988
|
|
2
|
On digraph polynomials, preprint dated December 3
– Chung, Graham
- 1993
|
|
2
|
Ordering the partition characters of the symmetric group
– Liebler, Vitale
- 1973
|
|
2
|
Problem 28, solution by
– Mantel
- 1907
|
|
2
|
A large family of chromatic polynomials
– Read
- 1981
|
|
1
|
Theory and Applications of Symmetric Functions
– Gasharov
- 1994
|
|
1
|
plane partitions, preprint dated 28
– Gessel, Viennot, et al.
- 1989
|
|
1
|
diagrams, Schur functions, the Gale-Ryser theorem and a conjecture of
– Lam, Young
- 1977
|
|
1
|
The Tutte polynomial of a hypermatroid, preprint
– Athanasiades
|
