中央研究院 数學研咒所 Combinatorial interpretations for a class of algebraic equations and uniform partitions Speaker: Yeong-Nan Yeh Institute of mathemetics academia sinica Aug21,2012
Combinatorial interpretations for a class of algebraic equations and uniform partitions Speaker: Yeong-Nan Yeh Institute of mathemetics, Academia sinica Aug. 21, 2012
中央研究院 数學研咒所 Catalan paths An n-Catalan path is a lattice path from(0,0 to(2n, O)in the first quadrant consisting of up step(l, 1)and down-step(1, -1) 第2页
第2页 Catalan paths • An n-Catalan path is a lattice path from (0,0) to (2n,0) in the first quadrant consisting of upstep (1,1) and down-step (1,-1)
中央研究院 数學研咒所 Catalan number (2n) for n>0 nn+1(n)-(7+1ln! 1,1,2,5,14,42,132,429,1430,4862,16796,, 第3页
第3页 Catanlan number 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, …
中央研究院 数學研咒所 Generating function: C(2)=22 ≥0 Algebaric equation C(z)=1+zC(z)2 第4页
第4页 2 ( ) 1 ( ) Algebaric equation : C z = + zC z = 0 Generating function : ( ) n n n C z c z
中央研究院 数學研咒所 Motzkin paths An n-Motizkin path is a lattice path from(, 0 to(n, O)in the first quadrant consisting of up step(1, 1), level-step(1, 0)and down-step(1, -1) Motzkin number:1,1,2,4,9,21,51,127,323,835,…, 第5页
第5页 Motzkin paths • An n-Motizkin path is a lattice path from (0,0) to (n,0) in the first quadrant consisting of upstep (1,1), level-step (1,0) and down-step (1,-1). Motzkin number:1, 1, 2, 4, 9, 21, 51, 127, 323, 835, …