Catalan series yog dab tsi?
Catalan series yog dab tsi?

Video: Catalan series yog dab tsi?

Video: Catalan series yog dab tsi?
Video: Veness Chang - Yog Hmoov Dlaab Tsi (Rendition) 2024, Kaum ib hlis
Anonim

Catalan Tus lej. Cov Catalan cov lej yog ib ntu ntawm cov lej zoo uas tshwm sim hauv ntau qhov teeb meem suav hauv combinatorics. Lawv suav qee yam ntawm txoj kab lattice, permutations, binary ntoo, thiab ntau lwm yam khoom sib xyaw.

Tsis tas li ntawd, tus lej Catalan yog dab tsi nrog piv txwv?

Catalan cov lej yog siv nyob rau hauv Wolfram Language li CatalanNumber[n]., 2, yog 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, (OEIS A000108). yog hypergeometric muaj nuj nqi.

Tsis tas li ntawd, muaj pes tsawg tus ntoo binary muaj nrog N nodes? Tag nrho cov muaj peev xwm Binary Nrhiav Ntoo nrog n txawv keys (countBST()) = Catalan tooj Cn = (2n)! / ((+ 1)! * !) Rau = 0, 1, 2, 3, … qhov tseem ceeb ntawm Catalan tus lej yog 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, …

Tsis tas li ntawd, Catalan tus lej suav li cas?

Catalan cov lej yog ib ntu ntawm cov zauv zoo, qhov twg nth lub sij hawm nyob rau hauv ib theem zuj zus, denoted Cn, yog pom nyob rau hauv cov nram qab no qauv :cn = (2n)! / ((n + 1)!

Pom zoo: