Connection Coefficients Between Generalized Rising and Falling Factorial Bases
نویسندگان
چکیده
منابع مشابه
Connection Coefficients Between Generalized Rising and Falling Factorial Bases
Let S = (s1, s2, . . .) be any sequence of nonnegative integers and let Sk = ∑k i=1 si We then define the falling (rising) factorials relative to S by setting (x)↓k,S= (x−S1)(x−S2) · · · (x−Sk) and (x)↑k,S= (x+S1)(x+S2) · · · (x+Sk) if k ≥ 1 with (x)↓0,S= (x)↑0,S= 1. It follows that {(x)↓k,S}k≥0 and {(x)↑k,S}k≥0 are bases for the polynomial ring Q[x]. We use a rook theory model due to Miceli an...
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ژورنال
عنوان ژورنال: Annals of Combinatorics
سال: 2015
ISSN: 0218-0006,0219-3094
DOI: 10.1007/s00026-015-0268-7