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2001, MSJ memoirs, ISBN 9784931469143, Volume 11., vii, 145
Book
Transactions of the American Mathematical Society, ISSN 0002-9947, 03/2007, Volume 359, Issue 3, pp. 1115 - 1128
We provide the first counterexamples to Neggers' 1978 conjecture and Stembridge's 1997 conjecture that the generating functions for descents and peaks in the... 
Equivalence relation | Integers | Mathematical theorems | Maps | Partially ordered sets | Information search | Polynomials | Counterexamples | Combinatorics | Vertices | POLYNOMIALS | MATHEMATICS
Journal Article
Advances in Mathematics, ISSN 0001-8708, 03/2012, Volume 229, Issue 4, pp. 2405 - 2414
A -graph for a Coxeter group is a combinatorial structure that encodes a module for the group algebra of , or more generally, a module for the associated... 
Kazhdan–Lusztig basis | W-graph | Strongly regular graph | Cell | Kazhdan-Lusztig basis | MATHEMATICS
Journal Article
Advances in Mathematics, ISSN 0001-8708, 2008, Volume 217, Issue 5, pp. 1935 - 1961
Coxeter cones are formed by intersecting the nonnegative sides of a collection of root hyperplanes in some root system. They are shellable subcomplexes of the... 
Unimodality | Coxeter complex | Graded poset | h-vector | Root system | Simplicial complex | MATHEMATICS | unimodality | root system | simplicial complex | graded poset | CONJECTURE
Journal Article
Journal of Combinatorial Theory, Series A, ISSN 0097-3165, 2007, Volume 114, Issue 7, pp. 1220 - 1237
We introduce the concept of irreducible circuits. In a vector arrangement , these are configurations consisting of one vector in the positive linear span of an... 
Vector arrangement | Oriented matroid | Root system | MATHEMATICS | root system | vector arrangement | oriented matroid
Journal Article
International Mathematics Research Notices, ISSN 1073-7928, 2007, Volume 2007
Journal Article
Advances in Applied Mathematics, ISSN 0196-8858, 01/2011, Volume 46, Issue 1-4, pp. 576 - 582
Young symmetrizers are primitive idempotents in the group algebra of the symmetric group that are indexed in a natural way by Young tableaux. Although the... 
Young symmetrizer | Young tableaux | MATHEMATICS, APPLIED | Tin | Partitions | Decomposition | Algebra | Mathematical analysis | Standards
Journal Article
Representation Theory, ISSN 1088-4165, 10/2008, Volume 12, Issue 1, pp. 346 - 368
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 02/1997, Volume 349, Issue 2, pp. 763 - 788
{ An (ordinary) P-partition is an order-preserving map from a partially ordered set to a chain, with special rules specifying where equal values may occur.... 
Integers | Equivalence relation | Partially ordered sets | Polynomials | Mathematical functions | Combinatorics | Tableaux | Product labeling | Vertices | MATHEMATICS | K PQ MATHEMATICS | SHIFTED TABLEAUX
Journal Article
Advances in Applied Mathematics, ISSN 0196-8858, 2010, Volume 44, Issue 3, pp. 203 - 224
A -graph is a weighted directed graph that encodes certain actions of a Coxeter group or the associated Iwahori–Hecke algebra . It is admissible if it is... 
W-graph | Kazhdan–Lusztig cell | Graph eigenvalues | Coxeter group | Kazhdan-Lusztig cell | MATHEMATICS, APPLIED | Algebra | Mathematical analysis | Classification | Graphs | Matrices | Matrix methods | Standards | Symmetry
Journal Article
Electronic Journal of Combinatorics, ISSN 1077-8926, 02/2005, Volume 11, Issue 2 R, pp. 1 - 41
It is a well-known theorem of Deodhar that the Bruhat ordering of a Coxeter group is the conjunction of its projections onto quotients by maximal parabolic... 
MATHEMATICS | MATHEMATICS, APPLIED | WEIGHT MULTIPLICITIES | SHELLABILITY | COXETER GROUPS
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 12/2003, Volume 355, Issue 12, pp. 4807 - 4823
We provide a simple list of axioms that characterize the crystal graphs of integrable highest weight modules for simply-laced quantum Kac-Moody algebras. 
Integers | Algebra | Axioms | Crystals | Partially ordered sets | Minimum value | Mathematical vectors | Vertices | Induction assumption | MATHEMATICS | ALGEBRAS | BASES | MODELS | GRAPHS
Journal Article
Representation Theory, ISSN 1088-4165, 2003, Volume 7, Issue 18, pp. 404 - 439
Journal Article
Journal of Algebraic Combinatorics, ISSN 0925-9899, 3/2007, Volume 25, Issue 2, pp. 141 - 148
We give a short, self-contained derivation of the Möbius function for the Bruhat orderings of Coxeter groups and their parabolic quotients. 
Convex and Discrete Geometry | Bruhat order | Mathematics | Group Theory and Generalizations | Order, Lattices, Ordered Algebraic Structures | Computer Science, general | Combinatorics | Coxeter group | Möbius function | MATHEMATICS | HECKE ALGEBRAS | coxeter group | Mobius function | COXETER GROUPS
Journal Article
Advances in Applied Mathematics, ISSN 0196-8858, 2009, Volume 42, Issue 4, pp. 423 - 444
Let be an irreducible affine Weyl group with Coxeter complex , where denotes the associated finite Weyl group and the translation subgroup. The Steinberg torus... 
Eulerian polynomial | Coxeter complex | γ-Nonnegativity | Descent statistic | MATHEMATICS, APPLIED | ALGEBRA | ENRICHED P-PARTITIONS | SYSTEMS | gamma-Nonnegativity | H-VECTORS | EULERIAN POLYNOMIALS
Journal Article
The Electronic Journal of Combinatorics, ISSN 1077-8926, 02/2005, p. R14
It is a well-known theorem of Deodhar that the Bruhat ordering of a Coxeter group is the conjunction of its projections onto quotients by maximal parabolic... 
Journal Article
Representation Theory, ISSN 1088-4165, 07/2004, Volume 8, Issue 11, pp. 267 - 289
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 04/1997, Volume 349, Issue 4, pp. 1285 - 1332
We analyze the structure of reduced expressions in the Coxeter groups A_{n}, B_{n} and D_{n}. Several special classes of elements are singled out for their... 
Integers | Commutativity | Braiding | Partially ordered sets | Coordinate systems | Mathematical functions | Polynomials | Tableaux | Induction assumption | Vertices | MATHEMATICS | K PQ MATHEMATICS | SCHUBERT POLYNOMIALS
Journal Article
Representation Theory, ISSN 1088-4165, 2006, Volume 10, Issue 1, p. 48
Journal Article
Journal of Algebraic Combinatorics, ISSN 0925-9899, 10/1996, Volume 5, Issue 4, pp. 353 - 385
Let W be a Coxeter group. We define an element w ε W to be fully commutative if any reduced expression for w can be obtained from any other by means of braid... 
Convex and Discrete Geometry | Bruhat order | Mathematics | Group Theory and Generalizations | Order, Lattices, Ordered Algebraic Structures | reduced word | weak order | Computer Science, general | Combinatorics | heap | Coxeter group | Weak order | Reduced word | Heap | MATHEMATICS | SCHUBERT POLYNOMIALS
Journal Article
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