TY - JOUR
T1 - More patterns in trees
T2 - Up and down, young and old, odd and even
AU - Dershowitz, Nachum
AU - Zaks, Shmuel
PY - 2008
Y1 - 2008
N2 - We apply the tree-pattern enumeration formulæ of earlier work of ours [N. Dershowitz and S. Zaks, Discrete Appl. Math., 25 (1989), pp. 241-255], and a new extension thereof, to some recent enumerations of distributions of leaves in ordered trees [W. Y. C. Chen, E. Deutsch, and S. Elizalde, European J. Combin., 27 (2006), pp. 414-427] and in bicolored ordered trees [L. H. Clark, J. E. McCanna, and L. A. Székely, Bull. Inst. Combin. Appl., 21 (1997), pp. 33-45], and of distributions of up-down-up subpaths in Dyck lattice paths [Y. Sun, Discrete Math., 287 (2004), pp. 177-186]. Bijections are used to facilitate the derivation of statistics for bicolored trees.
AB - We apply the tree-pattern enumeration formulæ of earlier work of ours [N. Dershowitz and S. Zaks, Discrete Appl. Math., 25 (1989), pp. 241-255], and a new extension thereof, to some recent enumerations of distributions of leaves in ordered trees [W. Y. C. Chen, E. Deutsch, and S. Elizalde, European J. Combin., 27 (2006), pp. 414-427] and in bicolored ordered trees [L. H. Clark, J. E. McCanna, and L. A. Székely, Bull. Inst. Combin. Appl., 21 (1997), pp. 33-45], and of distributions of up-down-up subpaths in Dyck lattice paths [Y. Sun, Discrete Math., 287 (2004), pp. 177-186]. Bijections are used to facilitate the derivation of statistics for bicolored trees.
KW - Bicolored trees
KW - Binary trees
KW - Bridges
KW - Dyck paths
KW - Lattice paths
KW - Node distribution
KW - Ordered trees
KW - Plane-planted trees
KW - Tree enumerations
KW - Tree patterns
UR - http://www.scopus.com/inward/record.url?scp=77952619383&partnerID=8YFLogxK
U2 - 10.1137/070687475
DO - 10.1137/070687475
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:77952619383
SN - 0895-4801
VL - 23
SP - 447
EP - 465
JO - SIAM Journal on Discrete Mathematics
JF - SIAM Journal on Discrete Mathematics
IS - 1
ER -