Mahir Bilen CAN, Lex E. RENNER

7686

Bruhat-Chevalley order on the rook monoid

The rook monoid Rn is the finite monoid whose elements are the 0-1 matrices with at most one nonzero entry in each row and column. The group of invertible elements of Rn is isomorphic to the symmetric group Sn. The natural extension to Rn of the Bruhat-Chevalley ordering on the symmetric group is defined in [1]. In this paper, we find an efficient, combinatorial description of the Bruhat-Chevalley ordering on Rn. We also give a useful, combinatorial formula for the length function on Rn.

Anahtar Kelimeler:

Rook monoid, Deodhar ordering, Bruhat-Chevalley ordering, Borel orbits

Bruhat-Chevalley order on the rook monoid

The rook monoid Rn is the finite monoid whose elements are the 0-1 matrices with at most one nonzero entry in each row and column. The group of invertible elements of Rn is isomorphic to the symmetric group Sn. The natural extension to Rn of the Bruhat-Chevalley ordering on the symmetric group is defined in [1]. In this paper, we find an efficient, combinatorial description of the Bruhat-Chevalley ordering on Rn. We also give a useful, combinatorial formula for the length function on Rn.

Keywords:

Rook monoid, Deodhar ordering, Bruhat-Chevalley ordering, Borel orbits,

Turkish Journal of Mathematics-Cover

ISSN: 1300-0098
Yayın Aralığı: 6
Yayıncı: TÜBİTAK

Arşiv

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Bruhat-Chevalley order on the rook monoid

Mahir Bilen CAN, Lex E. RENNER