Open AccessThe general $ \Gamma -$ compatible rook length polynomials
Author(s) -
Edward Arroyo,
Fangjun Arroyo
Publication year - 2010
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.41.2010.669
Subject(s) - mathematics , combinatorics , polynomial , algebraic number , connection (principal bundle) , discrete mathematics , geometry , mathematical analysis
Rook placements and rook polynomials have been studied by mathematicians since the early 1970's. Since then many relationships between rook placements and other subjects have been discovered (cf. [1], [6-15]). In [2] and [3], K. Ding introduced the rook length polynomials and the $ gamma - $compatible rook length polynomials. In [3] and [4], he used these polynomials to establish a connection between rook placements and algebraic geometry for the first time. In this paper, we give explicit formulas for the $ gamma - $compatible rook length polynomials in more general cases than considered in [3]. In particular, we generalize the formula for the rook length polynomial in the parabolic case in [2] to the $ gamma -$compatible rook length polynomial