<i>p</i>-nomial Coefficients and <i>p</i>-nomial Theorem
نویسندگان
چکیده
منابع مشابه
On multi F-nomial coefficients and Inversion formula for F-nomial coefficients
In response to [7], we discover the looked for inversion formula for F -nomial coefficients. Before supplying its proof, we generalize F -nomial coefficients to multi F -nomial coefficients and we give their combinatorial interpretation in cobweb posets language, as the number of maximal-disjoint blocks of the form σPk1,k2,...,ks of layer 〈Φ1 → Φn〉. Then we present inversion formula for F -nomi...
متن کاملOn multi F-nomial coefficients
In response to [6], we discover the looked for inversion formula for F -nomial coefficients. Before supplying its proof, we generalize F -nomial coefficients to multi F -nomial coefficients and we give their combinatorial interpretation in cobweb posets language, as the number of maximal-disjoint blocks of the form σPk1,k2,...,ks of layer 〈Φ1 → Φn〉. Then we present inversion formula for F -nomi...
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Let (Cn)n≥0 be the Lucas sequence Cn+2 = aCn+1 +bCn for all n ≥ 0, where C0 = 0 and C1 = 1. For 1 ≤ k ≤ m− 1 let [ m k ] C = CmCm−1 · · ·Cm−k+1 C1 · · ·Ck be the corresponding C-nomial coefficient. When Cn = Fn is the Fibonacci sequence (the numbers [ m k ] F are called Fibonomials), or Cn = (qn − 1)/(q − 1), where q > 1 is an integer (the numbers [ m k ] q are called q-binomial, or Gaussian co...
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In this paper, we consider a generalization of binomial coefficients, called C– nomial coefficients, dependent upon a sequence {un}n, with indices in arithmetic progressions. We obtain a general recurrence relation and a generating matrix, and point out some new relationships between these coefficients and the generalized Pascal matrices. Further, we obtain generating functions, combinatorial r...
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Abstract F-nomial coefficients encompass among others well-known binomial coefficients or Gaussian coefficients that count subsets of finite set and subspaces of finite vector space respectively. Here, the so called F-cobweb tiling sequences N(α) are considered. For such specific sequences a new interpretation with respect to Kwaśniewski general combinatorial interpretation of F -nomial coeffic...
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ژورنال
عنوان ژورنال: Turkish Journal of Analysis and Number Theory
سال: 2020
ISSN: 2333-1100
DOI: 10.12691/tjant-8-1-2