Restricted signed permutations counted by the Schröder numbers

Eric S. Egge

doi:10.1016/j.disc.2006.01.013

Restricted signed permutations counted by the Schröder numbers

Discrete Mathematics ◽

10.1016/j.disc.2006.01.013 ◽

2006 ◽

Vol 306 (6) ◽

pp. 552-563 ◽

Cited By ~ 1

Author(s):

Eric S. Egge

Keyword(s):

Signed Permutations ◽

Schröder Numbers

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On Sorting of Signed Permutations by Prefix and Suffix Reversals and Transpositions

Algorithms for Computational Biology - Lecture Notes in Computer Science ◽

10.1007/978-3-319-07953-0_12 ◽

2014 ◽

pp. 146-157 ◽

Cited By ~ 1

Author(s):

Carla Negri Lintzmayer ◽

Zanoni Dias

Keyword(s):

Signed Permutations

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Sorting Signed Permutations by Reversal (Reversal Distance)

Encyclopedia of Algorithms ◽

10.1007/978-0-387-30162-4_383 ◽

2008 ◽

pp. 858-860

Author(s):

David A. Bader

Keyword(s):

Signed Permutations

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Diagrams and Essential Sets for Signed Permutations

The Electronic Journal of Combinatorics ◽

10.37236/8106 ◽

2018 ◽

Vol 25 (3) ◽

Author(s):

David Anderson

Keyword(s):

Schubert Variety ◽

Signed Permutation ◽

Signed Permutations ◽

Degeneracy Locus ◽

Essential Set ◽

Diagrammatic Method ◽

Essential Sets ◽

Rank Conditions ◽

Theoretic Version

We introduce diagrams and essential sets for signed permutations, extending the analogous notions for ordinary permutations. In particular, we show that the essential set provides a minimal list of rank conditions defining the Schubert variety or degeneracy locus corresponding to a signed permutation. Our essential set is in bijection with the poset-theoretic version defined by Reiner, Woo, and Yong, and thus gives an explicit, diagrammatic method for computing the latter.

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