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Expansion of $k$-Schur functions for maximal $k$-rectangles within the affine nilCoxeter algebra
$k$-Schur functions $k$-rectangles affine nilCoxeter algebra Combinatorics
2011/9/14
Abstract: We give several explicit combinatorial formulas for the expansion of $k$-Schur functions indexed by maximal $k$-rectangles, $s_R^{(k)}$, in terms of the standard basis of the affine nilCoxet...
Linear algebra and bootstrap percolation
Bootstrap percolation linear algebra weak saturation
2011/8/29
Abstract: In $\HH$-bootstrap percolation, a set $A \subset [n]$ of initially `infected' vertices spreads by infecting vertices which are the only uninfected vertex in an edge of the hypergraph $\HH \s...
Weyl groups of fine gradings on matrix algebras, octonions and the Albert algebra
Graded algebra fine grading Weyl group octonions Albert algebra
2010/12/1
Given a grading : A = Lg2G Ag on a nonassociative algebra A by an abelian group G.
Infinite combinatorial issues raised by lifting problems in universal algebra
Algebra congruence variety critical point ladder morass Martin’s
2010/11/30
The critical point between varieties A and B of algebras is defined as the least cardinality of the semilattice of compact congruences of a member of A but of no member of B, if it exists.