A 55 Integers 10 ( 2010 ) , 771 - 792 a Left Weighted Catalan Extension
نویسنده
چکیده
There are many representations of the Catalan numbers. In this article, we will examine the ballot problem and extend it beyond the standard p-Catalan extension to a left weighted extension. This extension reduces naturally to the p-Catalan numbers (including the standard 2-Catalan numbers). We will then give a variety of examples of the extension for other representations of the Catalan numbers to demonstrate its general applicability.
منابع مشابه
What power of two divides a weighted Catalan number?
Given a sequence of integers b= (b0, b1, b2, . . .) one gives a Dyck path P of length 2n the weight wt(P )= bh1bh2 · · ·bhn, where hi is the height of the ith ascent of P . The corresponding weighted Catalan number is C n = ∑
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Given a sequence of integers b = (b0, b1, b2, . . .) one gives a Dyck path P of length 2n the weight wt(P ) = bh1bh2 · · · bhn , where hi is the height of the ith ascent of P . The corresponding weighted Catalan number is C n = ∑
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