| Popis: |
For any integer m ≥ 2 and a set V ⊂ { 1 , … , m } , let ( m , V ) denote the union of congruence classes of the elements in V modulo m . We study the Hankel determinants for the number of Dyck paths with peaks avoiding the heights in the set ( m , V ) . For any set V of even elements of an even modulo m , we give an explicit description of the sequence of Hankel determinants in terms of subsequences of arithmetic progression of integers. There are numerous instances for varied ( m , V ) with periodic sequences of Hankel determinants. We present a sufficient condition for the set ( m , V ) such that the sequence of Hankel determinants is periodic, including even and odd modulus m . |
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