caa a22 4500 445855495 CHVBK 20180317145426.0 cr unu---uuuuu 170323e20110301xx s 000 0 eng 10.1007/s00026-011-0082-9 doi (NATIONALLICENCE)springer-10.1007/s00026-011-0082-9 Elizalde Sergi Department of Mathematics, Dartmouth College, 03755, Hanover, NH, USA aut The X-Class and Almost-Increasing Permutations [Elektronische Daten] [Sergi Elizalde] In this paper we give a bijection between the class of permutations that can be drawn on an X-shape and a certain set of permutations that appears in Knuth [4] in connection to sorting algorithms. A natural generalization of this set leads us to the definition of almost-increasing permutations, which is a one-parameter family of permutations that can be characterized in terms of forbidden patterns. We find generating functions for almost-increasing permutations by using their cycle structure to map them to colored Motzkin paths. We also give refined enumerations with respect to the number of cycles, fixed points, excedances, and inversions. Springer Basel AG, 2011 cycle diagram nationallicence pattern-avoiding permutation nationallicence picture class nationallicence X-class nationallicence Annals of Combinatorics SP Birkhäuser Verlag Basel 15/1(2011-03-01), 51-68 0218-0006 15:1<51 2011 15 26 https://doi.org/10.1007/s00026-011-0082-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00026-011-0082-9 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Elizalde Sergi Department of Mathematics, Dartmouth College, 03755, Hanover, NH, USA aut NATIONALLICENCE 773 0- Annals of Combinatorics SP Birkhäuser Verlag Basel 15/1(2011-03-01), 51-68 0218-0006 15:1<51 2011 15 26 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer