caa a22 4500 605461465 CHVBK 20210128100243.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s10114-015-5153-0 doi (NATIONALLICENCE)springer-10.1007/s10114-015-5153-0 On pattern avoiding flattened set partitions [Elektronische Daten] [Thomas Liu, Andy Zhang] Let Π = B 1/B 2/ ··· /B k be any set partition of [n] = {1, 2,..., n} satisfying that entries are increasing in each block and blocks are arranged in increasing order of their first entries. Then Callan defined the flattened Π to be the permutation of [n] obtained by erasing the divers between its blocks, and Callan also enumerated the number of set partitions of [n] whose flattening avoids a single 3-letter pattern. Mansour posed the question of counting set partitions of [n] whose flattening avoids a pattern of length 4. In this paper, we present the number of set partitions of [n] whose flattening avoids one of the patterns: 1234, 1243, 1324, 1342, 1423, 1432, 3142 and 4132. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg, 2015 Set partition nationallicence pattern avoidance nationallicence flattened partition nationallicence Liu Thomas Department of Foundation Courses, Southwest Jiaotong University, 614202, Emeishan, Sichuan, P. R. China aut Zhang Andy Center for Combinatorics, LPMC-TJKLC, Nankai University, 300071, Tianjin, P. R. China aut Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/12(2015-12-01), 1923-1928 1439-8516 31:12<1923 2015 31 10114 https://doi.org/10.1007/s10114-015-5153-0 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10114-015-5153-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Liu Thomas Department of Foundation Courses, Southwest Jiaotong University, 614202, Emeishan, Sichuan, P. R. China aut NATIONALLICENCE 700 1- Zhang Andy Center for Combinatorics, LPMC-TJKLC, Nankai University, 300071, Tianjin, P. R. China aut NATIONALLICENCE 773 0- Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/12(2015-12-01), 1923-1928 1439-8516 31:12<1923 2015 31 10114