منابع مشابه
Rook Theory and t-Cores
If t is a positive integer, then a partition of a non-negative integer n is a t−core if none of the hook numbers of the associated Ferrers-Young diagram is a multiple of t. These partitions arise in the representation theory of finite groups and also in the theory of class numbers. We prove that if t = 2, 3, or 4, then two different t−cores are rook equivalent if and only if they are conjugates...
متن کاملNON-CONJUGATE, ROOK EQUIVALENT t-CORES
Consider a partition of a natural number n. The partition is called a t-core if each of the hook numbers (one more than the number of squares to the right and below a certain node of n) from its Ferrers board is not divisible by t. [HOS98] conjectured in 1998 that if t ≥ 5, then there exists a constant Nt such that for every positive integer n ≥ Nt , there exist two distinct rook equivalent t-c...
متن کاملRook Theory and Hypergeometric Series
The number of ways of placing k non-attacking rooks on a Ferrers board is expressed as a hypergeometric series, of a type originally studied by Karlsson and Minton. Known transformation identities for series of this type translate into new theorems about rook polynomials.
متن کاملRook Theory, Compositions, and Zeta Functions
A new family of Dirichlet series having interesting combinatorial properties is introduced. Although they have no functional equation or Euler product, under the Riemann Hypothesis it is shown that these functions have no zeros in Re(s) > 1/2. Some identities in the ring of formal power series involving rook theory and continued fractions are developed.
متن کاملRepresentation theory of q-rook monoid algebras
We show that, over an arbitrary field, q-rook monoid algebras are iterated inflations of Iwahori-Hecke algebras, and, in particular, are cellular. Furthermore we give an algebra decomposition which shows a q-rook monoid algebra is Morita equivalent to a direct sum of Iwahori-Hecke algebras. We state some of the consequences for the representation theory of q-rook monoid algebras.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1998
ISSN: 0097-3165
DOI: 10.1006/jcta.1998.2874