Hilbert series of the Grassmannian and k-Narayana numbers
نویسندگان
چکیده
منابع مشابه
Narayana numbers and Schur-Szego composition
In the present paper we find a new interpretation of Narayana polynomials Nn(x) which are the generating polynomials for the Narayana numbers Nn,k = 1 n C k−1 n C k n where C i j stands for the usual binomial coefficient, i.e. C j = j! i!(j−i)! . They count Dyck paths of length n and with exactly k peaks, see e.g. [13] and they appeared recently in a number of different combinatorial situations...
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Using Kummer’s theorem, we give a necessary and sufficient condition for a Narayana number to be divisible by a given prime. We use this to derive certain properties of the Narayana triangle. 1 The main theorem Let N denote the nonnegative integers and let k, n ∈ N. The Narayana numbers [10, A001263] can be defined as N(n, k) = 1 n (
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ژورنال
عنوان ژورنال: Communications in Mathematics
سال: 2019
ISSN: 2336-1298
DOI: 10.2478/cm-2019-0003