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Lexicographic Shellability of Partial Involutions
Lexicographic Shellability of Partial Involutions Combinatorics Algebraic Geometry
2012/5/9
In this manuscript we study inclusion posets of Borel orbit closures on (symmetric) matrices. In particular, we show that the Bruhat poset of partial involutions is a lexicographiically shellable pose...
The set of autotopisms of partial Latin squares
Partial Latin square autotopism group cycle structure
2011/9/13
Abstract: Symmetries of a partial Latin square are determined by its autotopism group. Analogously to the case of Latin squares, given an isotopism $\Theta$, the cardinality of the set $\mathcal{PLS}_...
Hall's Condition for Partial Latin Squares
Hall's Condition Partial Latin Squares Combinatorics
2011/9/5
Abstract: Hall's Condition is a necessary condition for a partial latin square to be completable. Hilton and Johnson showed that for a partial latin square whose filled cells form a rectangle, Hall's ...
An analogue of Ryser's Theorem for partial Sudoku squares
Ryser's Theorem partial Sudoku squares analogue Combinatorics
2011/9/5
Abstract: In 1956 Ryser gave a necessary and sufficient condition for a partial latin rectangle to be completable to a latin square. In 1990 Hilton and Johnson showed that Ryser's condition could be r...
The complex of partial bases for F_n and finite generation of the Torelli subgroup of Aut(F_n)
partial bases for F_n finite generation Torelli subgroup of Aut(F_n)
2011/1/19
We study the complex of partial bases of a free group, which is an analogue for Aut(Fn)
of the curve complex for the mapping class group. We prove that it is connected and simply
connected, and we a...