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%I A073200
%S A073200 0,1,0,3,1,0,2,2,1,0,7,3,3,1,0,8,4,2,3,1,0,6,6,8,2,3,1,0,4,5,7,7,2,3,1,0,5,7,6,6,
%T A073200 8,2,3,1,0,17,8,5,8,7,7,2,2,1,0,18,9,4,4,6,8,7,3,3,1,0,20,10,22,5,5,5,8,4,2,2,1,0,21,14,
%U A073200 21,17,4,4,6,5,8,3,3,1,0
%N A073200 Array of permutations of N, induced by the gatomorphisms of the simple type B, constructed by simple recursive process from the primitive gatomorphisms A069770 and A072796.
%R A073200
%H A073200 A. Karttunen, <A HREF="http://www.megabaud.fi/~karttu/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</A>
%O A073200 0,4
%K A073200 nonn,tabl
%A A073200 Antti.Karttunen (my_firstname.my_surname@iki.fi) MMM DD 2002
%Y A073200 Four other tables giving the corresponding cycle-counts: A073201, counts of the fixed elements: A073202, the lengths of the largest cycles: A073203, the LCM's of all the cycles: A073204.
%Y A073200 The first 21 rows of this table:
%Y A073200 Row 0: A069770. Row 1: A072796. Row 2: A057163. Row 3: A073269, Row 4: A057163 (duplicate), Row 5: A073270, Row 6: A069767, Row 7: A001477 (identity perm.), Row 8: A069768, Row 9: A073280.
%Y A073200  Row 10: A069770 (dupl.), Row 11: A072796 (dupl.), Row 12: A057511, Row 13: A073282,  Row 14: A057512, Row 15: A073281, Row 16: A057509, Row 17: A073280 (dupl.), Row 18: A057510, Row 19: A073283, Row 20: A073284.
%Y A073200 Other gatomorphism-induced EIS-permutations which occur in this table. Only the first known occurrence is given. Involutions are marked with *, others paired with their inverse:
%Y A073200 Row 164: A057164*, Row 168: A057508*, Row 179: A072797*
%Y A073200 Row 41: A073286 - Row 69: A073287. Row 105: A073290 - Row 197: A073291. Row 416: A073288 - Row 696: A073289. 
%Y A073200 Row 261: A057501 - Row 521: A057502. Row 2618: A057503 - Row 5216: A057504. Row 2614: A057505 - Row 5212: A057506
%Y A073200 Row 10435: A073292 - Row ...: A073293. Row 17517: A057161 - Row ...: A057162.
%D A073200
%p A073200


%I A073201
%S A073201 1,1,1,1,1,1,3,2,1,1,7,4,1,1,1,22,11,3,1,1,1,66,31,7,2,1,1,1,217,96,22,4,3,1,1,1,715,305,66,
%T A073201 11,7,2,1,1,1,2438,1007,217,30,22,4,2,2,1,1,8398,3389,715,93,66,11,3,5,1,1,1,29414,11636,2438,
%U A073201 292,217,30,6,14,2,2,1,1,104006,40498,8398,965,715,93,12,42,3,3,1,1,1
%N A073201 Array of cycle counts for the table A073200.
%R A073201
%H A073201 A. Karttunen, <A HREF="http://www.megabaud.fi/~karttu/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</A>
%O A073201 0,7
%K A073201 nonn,tabl
%A A073201 Antti.Karttunen (my_firstname.my_surname@iki.fi) MMM DD 2002
%Y A073201 Few EIS-sequences which occur in this table. Only the first known occurrence(s) given (marked with ? if not yet proven/unclear):
%Y A073201 Rows 0, 2, 4, etc.: A007595, Row 1: A073191, Row 7: A000108, Rows 12, 14, 20, ...: A057513, Rows 16, 18, ...: A003239, Row 57, ..., 164: A007123?, Row 168: A073193, Row 261: A002995, Row 2614: A057507, Row 2618 (?), row 17517: A001683
%D A073201
%p A073201


%I A073202
%S A073202 1,1,1,0,1,1,1,2,1,1,0,3,0,1,1,2,8,1,0,1,1,0,20,0,0,0,1,1,5,60,2,0,1,0,1,1,0,181,0,0,
%T A073202 0,0,0,1,1,14,584,5,0,2,0,1,2,1,1,0,1916,0,0,0,0,0,5,0,1,1,42,6476,14,0,5,0,0,14,1,2,1,1,0,
%U A073202 22210,0,0,0,0,0,42,0,1,0,1,1
%N A073202 Array of fixed elements counts for the table A073200.
%R A073202
%H A073202 A. Karttunen, <A HREF="http://www.megabaud.fi/~karttu/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</A>
%O A073202 0,8
%K A073202 nonn,tabl
%A A073202 Antti.Karttunen (my_firstname.my_surname@iki.fi) MMM DD 2002
%Y A073202 Few EIS-sequences which occur in this table. Only the first known occurrence(s) given (marked with ? if not yet proven/unclear):
%Y A073202 Rows 0, 2, 4, etc.: "Aerated Catalans" shifted right and prepended with 1 (Cf. A000108), Row 1: A0073190, Rows 3, 5, 261, 2614, 2618, 17517, etc: A019590 but with offset 0 instead of 1 (means that the gatomorphisms like A073269, A073270, A057501, A057505, A057503 and A057161 never fix any Catalan structure of size larger than 1)
&Y A073202 Row 6: A036987, Row 7: A000108, Rows 12, 14, 20, ...: A057546, Rows 16, 18: A034731, Row 41: A073268, Row 105: essentially A073267, Row 57, ..., 164: A001405, Row 168: A073192, Row 416: essentially A023359 ?, Row 10435: also A036987.
%D A073202
%p A073202


%I A073203
%S A073203 1,1,1,2,1,1,2,1,1,1,2,2,2,1,1,2,2,2,2,1,1,2,2,2,3,2,1,1,2,2,2,6,2,2,1,1,2,2,2,8,
%T A073203 2,3,2,1,1,2,2,2,10,2,6,4,1,1,1,2,2,2,12,2,8,8,1,2,1,1,2,2,2,14,2,10,16,1,4,1,1,1,2,2,
%U A073203 2,16,2,12,32,1,8,2,2,1,1
%N A073203 Array of max. cycle length sequences for the table A073200.
%R A073203
%H A073203 A. Karttunen, <A HREF="http://www.megabaud.fi/~karttu/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</A>
%O A073203 0,4
%K A073203 nonn,tabl
%A A073203 Antti.Karttunen (my_firstname.my_surname@iki.fi) MMM DD 2002
%Y A073203 Few EIS-sequences which occur in this table. Only the first known occurrence(s) given:
%Y A073203 Rows 6 & 8: A011782, Row 7: A000012, Row 12, 14: A000793 (shifted right and prepended with 1), Row 261: A057543, Row 2614: A057545, Rows 2618, 17517: A057544.
%D A073203
%p A073203


%I A073204
%S A073204 1,1,1,2,1,1,2,1,1,1,2,2,2,1,1,2,2,2,2,1,1,2,2,2,6,2,1,1,2,2,2,12,2,2,1,1,2,2,2,120,
%T A073204 2,6,2,1,1,2,2,2,120,2,12,4,1,1,1,2,2,2,840,2,120,8,1,2,1,1,2,2,2,840,2,120,16,1,4,1,1,1,2,
%U A073204 2,2,5040,2,840,32,1,8,2,2,1,1
%N A073204 Array of sequences, each giving the least common multiples of all cycle lengths ... for the table A073200.
%R A073204
%H A073204 A. Karttunen, <A HREF="http://www.megabaud.fi/~karttu/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</A>
%O A073204 0,4
%K A073204 nonn,tabl
%A A073204 Antti.Karttunen (my_firstname.my_surname@iki.fi) MMM DD 2002
%Y A073204 Few EIS-sequences which occur in this table. Only the first known occurrence(s) given:
%Y A073204 Rows 6 & 8: A011782, Row 7: A000012, Row 2614: A060114, Row 2618 (?), ..., 17517: A057544
%D A073204
%p A073204