\BOOKMARK [1][-]{section.1}{Introduction}{}% 1
\BOOKMARK [2][-]{subsection.1.1}{Encodings of permutations}{section.1}% 2
\BOOKMARK [2][-]{subsection.1.2}{Operations on inversion sequences}{section.1}% 3
\BOOKMARK [2][-]{subsection.1.3}{Statistics on inversion sequences}{section.1}% 4
\BOOKMARK [2][-]{subsection.1.4}{Ultimately constant avoidance sequences}{section.1}% 5
\BOOKMARK [1][-]{section.2}{Patterns whose sequences appear in the OEIS}{}% 6
\BOOKMARK [2][-]{subsection.2.1}{Classes 7\(A,B,C,D\): n}{section.2}% 7
\BOOKMARK [2][-]{subsection.2.2}{Classes 12\(A,B\): 2\(n-1\) for n>1}{section.2}% 8
\BOOKMARK [2][-]{subsection.2.3}{Class 21: Fn+1}{section.2}% 9
\BOOKMARK [2][-]{subsection.2.4}{Classes 22\(A,B,C\): Lazy caterer sequence, n \(\)2 +1}{section.2}% 10
\BOOKMARK [3][-]{subsubsection.2.4.1}{Class 22A: Avoiding ei < ej =ek}{subsection.2.4}% 11
\BOOKMARK [3][-]{subsubsection.2.4.2}{Class 22B: Avoiding ei < ej and ei < ek}{subsection.2.4}% 12
\BOOKMARK [3][-]{subsubsection.2.4.3}{Class 22C: Avoiding ei ej =ek}{subsection.2.4}% 13
\BOOKMARK [2][-]{subsection.2.5}{Classes 33\(A,B\): Fn+2-1}{section.2}% 14
\BOOKMARK [3][-]{subsubsection.2.5.1}{Class 33A: Avoiding ei = ej ek}{subsection.2.5}% 15
\BOOKMARK [3][-]{subsubsection.2.5.2}{Class 33B: Avoiding ei ej ek and ei =ek}{subsection.2.5}% 16
\BOOKMARK [2][-]{subsection.2.6}{Classes 64\(A,B,C,D\): 2n-1}{section.2}% 17
\BOOKMARK [3][-]{subsubsection.2.6.1}{Class 64A: Avoiding ei = ej < ek}{subsection.2.6}% 18
\BOOKMARK [3][-]{subsubsection.2.6.2}{Class 64B: Avoiding ei<ejek}{subsection.2.6}% 19
\BOOKMARK [3][-]{subsubsection.2.6.3}{Class 64C: Avoiding ei<ej ek}{subsection.2.6}% 20
\BOOKMARK [3][-]{subsubsection.2.6.4}{Class 64D: Avoiding ei ej = ek}{subsection.2.6}% 21
\BOOKMARK [2][-]{subsection.2.7}{Classes 121\(A,B,C\): Grassmannian permutations, 2n-n}{section.2}% 22
\BOOKMARK [3][-]{subsubsection.2.7.1}{Class 121A: Avoiding ei=ej < ek}{subsection.2.7}% 23
\BOOKMARK [3][-]{subsubsection.2.7.2}{Class 121B: Avoiding ei=ej =ek and ei =ek}{subsection.2.7}% 24
\BOOKMARK [3][-]{subsubsection.2.7.3}{Class 121C: Avoiding ej ek \040and ei =ek }{subsection.2.7}% 25
\BOOKMARK [2][-]{subsection.2.8}{Class 151: 321-avoiding separable permutations}{section.2}% 26
\BOOKMARK [2][-]{subsection.2.9}{Class 185: 321-avoiding vexillary permutations, 2n+1-n+1 \(\)3-2n-1 }{section.2}% 27
\BOOKMARK [2][-]{subsection.2.10}{Class 187: Conjectured to be counted by A049125}{section.2}% 28
\BOOKMARK [2][-]{subsection.2.11}{Class 193: Sn\(132,4312\), \(n-1\)2n-2 +1}{section.2}% 29
\BOOKMARK [2][-]{subsection.2.12}{Class 233: In\(012\), F2n-1}{section.2}% 30
\BOOKMARK [2][-]{subsection.2.13}{Class 304: Conjectured to be counted by A229046}{section.2}% 31
\BOOKMARK [2][-]{subsection.2.14}{Classes 429\(A,B,C\): Catalan numbers}{section.2}% 32
\BOOKMARK [3][-]{subsubsection.2.14.1}{Class 429A: Avoiding ej > ek}{subsection.2.14}% 33
\BOOKMARK [3][-]{subsubsection.2.14.2}{Class 429B: Avoiding ej ek and ei <ek}{subsection.2.14}% 34
\BOOKMARK [3][-]{subsubsection.2.14.3}{Class 429C: Avoiding ei ej \040and ei ek }{subsection.2.14}% 35
\BOOKMARK [2][-]{subsection.2.15}{Class 523: Sn\( \040542\) and the nexus numbers}{section.2}% 36
\BOOKMARK [2][-]{subsection.2.16}{Classes 772\(A,B\): Set partitions avoiding enhanced 3-crossings}{section.2}% 37
\BOOKMARK [2][-]{subsection.2.17}{Classes 877\(A,B,C,D\): Bell numbers and Stirling numbers}{section.2}% 38
\BOOKMARK [3][-]{subsubsection.2.17.1}{Class 877A: Avoiding ei < ej =ek}{subsection.2.17}% 39
\BOOKMARK [3][-]{subsubsection.2.17.2}{Class 877B: Avoiding ei = ej ek}{subsection.2.17}% 40
\BOOKMARK [3][-]{subsubsection.2.17.3}{Class 877C: Avoiding \040ei =ej =ek and ei=ek}{subsection.2.17}% 41
\BOOKMARK [3][-]{subsubsection.2.17.4}{Class 877D: Avoiding ei ej and ei=ek}{subsection.2.17}% 42
\BOOKMARK [2][-]{subsection.2.18}{Class 924: Central binomial coefficients}{section.2}% 43
\BOOKMARK [2][-]{subsection.2.19}{Class 1064: Conjectured to be counted by A071356}{section.2}% 44
\BOOKMARK [2][-]{subsection.2.20}{Class 1265: Sn\(2143,3142,4132\) }{section.2}% 45
\BOOKMARK [2][-]{subsection.2.21}{Class 1347: Conjectured to be counted by Sn\(4123,4132,4213\)}{section.2}% 46
\BOOKMARK [2][-]{subsection.2.22}{Class 1385: In\(000\) and the Euler up/down numbers}{section.2}% 47
\BOOKMARK [2][-]{subsection.2.23}{Class 1694: In\(102\)}{section.2}% 48
\BOOKMARK [2][-]{subsection.2.24}{1806\(A,B,C,D\): large Schr\366der numbers}{section.2}% 49
\BOOKMARK [3][-]{subsubsection.2.24.1}{Class 1806A: Avoiding ej > ek and ei < ek}{subsection.2.24}% 50
\BOOKMARK [3][-]{subsubsection.2.24.2}{Class 1806B: Avoiding ei > ej and ei ek }{subsection.2.24}% 51
\BOOKMARK [3][-]{subsubsection.2.24.3}{Class 1806C: Avoiding ei ej and ei >ek}{subsection.2.24}% 52
\BOOKMARK [3][-]{subsubsection.2.24.4}{Class 1806D: Avoiding ei ej = ek and ei ek}{subsection.2.24}% 53
\BOOKMARK [2][-]{subsection.2.25}{Class 2074: Baxter numbers}{section.2}% 54
\BOOKMARK [2][-]{subsection.2.26}{Classes 2549\(A,B,C\): Conjectured to be counted by Sn\(4231,42513\)}{section.2}% 55
\BOOKMARK [2][-]{subsection.2.27}{Classes 2958\(A,B,C,D\): Plane permutations and the semi-Baxter numbers}{section.2}% 56
\BOOKMARK [3][-]{subsubsection.2.27.1}{Class 2958A: Avoiding ej < ek and \040eiek}{subsection.2.27}% 57
\BOOKMARK [3][-]{subsubsection.2.27.2}{Class 2958B: Avoiding ei > ej ek}{subsection.2.27}% 58
\BOOKMARK [3][-]{subsubsection.2.27.3}{Class 2958C: Avoiding ei ej > ek}{subsection.2.27}% 59
\BOOKMARK [3][-]{subsubsection.2.27.4}{2958D: Avoiding ej ek and ei > ek}{subsection.2.27}% 60
\BOOKMARK [2][-]{subsection.2.28}{Classes 3207\(A,B\): In\(101\), In\(110\) }{section.2}% 61
\BOOKMARK [2][-]{subsection.2.29}{Class 3720: Quadrant Marked Mesh Patterns}{section.2}% 62
\BOOKMARK [2][-]{subsection.2.30}{Class 5040: n!}{section.2}% 63
\BOOKMARK [1][-]{section.3}{Results about patterns whose sequences don't appear in the OEIS Sloane}{}% 64
\BOOKMARK [2][-]{subsection.3.1}{Counting results}{section.3}% 65
\BOOKMARK [3][-]{subsubsection.3.1.1}{Class 805: Avoiding ei ej > ek and ei =ek}{subsection.3.1}% 66
\BOOKMARK [3][-]{subsubsection.3.1.2}{Class 1016: Avoiding ei > ej and ei = ek}{subsection.3.1}% 67
\BOOKMARK [3][-]{subsubsection.3.1.3}{1079\(A,B\): sum of binomial coefficients}{subsection.3.1}% 68
\BOOKMARK [3][-]{subsubsection.3.1.4}{4306A,B: In\(210\), In\(201\)}{subsection.3.1}% 69
\BOOKMARK [2][-]{subsection.3.2}{Wilf-equivalence results}{section.3}% 70
\BOOKMARK [3][-]{subsubsection.3.2.1}{Class 1953A: Avoiding ej>ek and ei>ek, and Class 1953B: Avoiding ei =ej ek and ei>ek}{subsection.3.2}% 71
\BOOKMARK [3][-]{subsubsection.3.2.2}{Class 1833A: Avoiding ej =ek and ei>ek, and Class 1833B: Avoiding ei =ej and ei>ek}{subsection.3.2}% 72
\BOOKMARK [3][-]{subsubsection.3.2.3}{Class 746A: Avoiding ej > ek and ei ek, and Class 746B: Avoiding ei =ej ek and ei ek}{subsection.3.2}% 73
\BOOKMARK [3][-]{subsubsection.3.2.4}{Class 663A: Avoiding ej =ek and \040ei ek, and Class 663B: Avoiding ei =ej and ei ek}{subsection.3.2}% 74
\BOOKMARK [1][-]{section.4}{Concluding remarks}{}% 75
\BOOKMARK [1][-]{section.5}{Acknowledgments}{}% 76