NON-CONJUGATE, ROOK EQUIVALENT t-CORES
نویسنده
چکیده
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-cores of n which are not conjugate. In 2003, Anderson proved [And04] that this conjecture is true for t ≥ 12 with Nt = 4. The goal of this 2009 research was to investigate the situation when 5 ≤ t ≤ 11. What follows is a collection of lemmas, corollaries, and conjectures that resulted from this research.
منابع مشابه
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