Congruences and relations for r-Fishburn numbers
نویسنده
چکیده
Recently Andrews and Sellers proved some amazing congruences for the Fishburn numbers. We extend their results to a more general sequence of numbers. As a result we prove a new congruence mod 23 for the Fishburn numbers and prove their conjectured mod 5 congruence for a related sequence. We also extend and prove some unpublished conjectures of Garthwaite and Rhoades.
منابع مشابه
Congruences for the Fishburn Numbers
The Fishburn numbers, ξ(n), are defined by a formal power series expansion ∞ ∑ n=0 ξ(n)q = 1 + ∞ ∑ n=1 n ∏ j=1 (1− (1− q)). For half of the primes p, there is a non–empty set of numbers T (p) lying in [0, p− 1] such that if j ∈ T (p), then for all n ≥ 0, ξ(pn+ j) ≡ 0 (mod p). 2010 Mathematics Subject Classification: 05A19, 11F20, 11P83
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عنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 134 شماره
صفحات -
تاریخ انتشار 2015