Identifier
Mp00093: Dyck paths to binary wordBinary words
Mp00158: Binary words alternating inverseBinary words
Mp00104: Binary words reverseBinary words
Images
=>
Cc0005;cc-rep-0
[1,0]=>10=>11=>11 [1,0,1,0]=>1010=>1111=>1111 [1,1,0,0]=>1100=>1001=>1001 [1,0,1,0,1,0]=>101010=>111111=>111111 [1,0,1,1,0,0]=>101100=>111001=>100111 [1,1,0,0,1,0]=>110010=>100111=>111001 [1,1,0,1,0,0]=>110100=>100001=>100001 [1,1,1,0,0,0]=>111000=>101101=>101101 [1,0,1,0,1,0,1,0]=>10101010=>11111111=>11111111 [1,0,1,0,1,1,0,0]=>10101100=>11111001=>10011111 [1,0,1,1,0,0,1,0]=>10110010=>11100111=>11100111 [1,0,1,1,0,1,0,0]=>10110100=>11100001=>10000111 [1,0,1,1,1,0,0,0]=>10111000=>11101101=>10110111 [1,1,0,0,1,0,1,0]=>11001010=>10011111=>11111001 [1,1,0,0,1,1,0,0]=>11001100=>10011001=>10011001 [1,1,0,1,0,0,1,0]=>11010010=>10000111=>11100001 [1,1,0,1,0,1,0,0]=>11010100=>10000001=>10000001 [1,1,0,1,1,0,0,0]=>11011000=>10001101=>10110001 [1,1,1,0,0,0,1,0]=>11100010=>10110111=>11101101 [1,1,1,0,0,1,0,0]=>11100100=>10110001=>10001101 [1,1,1,0,1,0,0,0]=>11101000=>10111101=>10111101 [1,1,1,1,0,0,0,0]=>11110000=>10100101=>10100101 [1,0,1,0,1,0,1,0,1,0]=>1010101010=>1111111111=>1111111111 [1,0,1,0,1,0,1,1,0,0]=>1010101100=>1111111001=>1001111111 [1,0,1,0,1,1,0,0,1,0]=>1010110010=>1111100111=>1110011111 [1,0,1,0,1,1,0,1,0,0]=>1010110100=>1111100001=>1000011111 [1,0,1,0,1,1,1,0,0,0]=>1010111000=>1111101101=>1011011111 [1,0,1,1,0,0,1,0,1,0]=>1011001010=>1110011111=>1111100111 [1,0,1,1,0,0,1,1,0,0]=>1011001100=>1110011001=>1001100111 [1,0,1,1,0,1,0,0,1,0]=>1011010010=>1110000111=>1110000111 [1,0,1,1,0,1,0,1,0,0]=>1011010100=>1110000001=>1000000111 [1,0,1,1,0,1,1,0,0,0]=>1011011000=>1110001101=>1011000111 [1,0,1,1,1,0,0,0,1,0]=>1011100010=>1110110111=>1110110111 [1,0,1,1,1,0,0,1,0,0]=>1011100100=>1110110001=>1000110111 [1,0,1,1,1,0,1,0,0,0]=>1011101000=>1110111101=>1011110111 [1,0,1,1,1,1,0,0,0,0]=>1011110000=>1110100101=>1010010111 [1,1,0,0,1,0,1,0,1,0]=>1100101010=>1001111111=>1111111001 [1,1,0,0,1,0,1,1,0,0]=>1100101100=>1001111001=>1001111001 [1,1,0,0,1,1,0,0,1,0]=>1100110010=>1001100111=>1110011001 [1,1,0,0,1,1,0,1,0,0]=>1100110100=>1001100001=>1000011001 [1,1,0,0,1,1,1,0,0,0]=>1100111000=>1001101101=>1011011001 [1,1,0,1,0,0,1,0,1,0]=>1101001010=>1000011111=>1111100001 [1,1,0,1,0,0,1,1,0,0]=>1101001100=>1000011001=>1001100001 [1,1,0,1,0,1,0,0,1,0]=>1101010010=>1000000111=>1110000001 [1,1,0,1,0,1,0,1,0,0]=>1101010100=>1000000001=>1000000001 [1,1,0,1,0,1,1,0,0,0]=>1101011000=>1000001101=>1011000001 [1,1,0,1,1,0,0,0,1,0]=>1101100010=>1000110111=>1110110001 [1,1,0,1,1,0,0,1,0,0]=>1101100100=>1000110001=>1000110001 [1,1,0,1,1,0,1,0,0,0]=>1101101000=>1000111101=>1011110001 [1,1,0,1,1,1,0,0,0,0]=>1101110000=>1000100101=>1010010001 [1,1,1,0,0,0,1,0,1,0]=>1110001010=>1011011111=>1111101101 [1,1,1,0,0,0,1,1,0,0]=>1110001100=>1011011001=>1001101101 [1,1,1,0,0,1,0,0,1,0]=>1110010010=>1011000111=>1110001101 [1,1,1,0,0,1,0,1,0,0]=>1110010100=>1011000001=>1000001101 [1,1,1,0,0,1,1,0,0,0]=>1110011000=>1011001101=>1011001101 [1,1,1,0,1,0,0,0,1,0]=>1110100010=>1011110111=>1110111101 [1,1,1,0,1,0,0,1,0,0]=>1110100100=>1011110001=>1000111101 [1,1,1,0,1,0,1,0,0,0]=>1110101000=>1011111101=>1011111101 [1,1,1,0,1,1,0,0,0,0]=>1110110000=>1011100101=>1010011101 [1,1,1,1,0,0,0,0,1,0]=>1111000010=>1010010111=>1110100101 [1,1,1,1,0,0,0,1,0,0]=>1111000100=>1010010001=>1000100101 [1,1,1,1,0,0,1,0,0,0]=>1111001000=>1010011101=>1011100101 [1,1,1,1,0,1,0,0,0,0]=>1111010000=>1010000101=>1010000101 [1,1,1,1,1,0,0,0,0,0]=>1111100000=>1010110101=>1010110101 [1,0,1,0,1,0,1,0,1,0,1,0]=>101010101010=>111111111111=>111111111111 [1,0,1,0,1,0,1,0,1,1,0,0]=>101010101100=>111111111001=>100111111111 [1,0,1,0,1,0,1,1,0,0,1,0]=>101010110010=>111111100111=>111001111111 [1,0,1,0,1,0,1,1,0,1,0,0]=>101010110100=>111111100001=>100001111111 [1,0,1,0,1,0,1,1,1,0,0,0]=>101010111000=>111111101101=>101101111111 [1,0,1,0,1,1,0,0,1,0,1,0]=>101011001010=>111110011111=>111110011111 [1,0,1,0,1,1,0,0,1,1,0,0]=>101011001100=>111110011001=>100110011111 [1,0,1,0,1,1,0,1,0,0,1,0]=>101011010010=>111110000111=>111000011111 [1,0,1,0,1,1,0,1,0,1,0,0]=>101011010100=>111110000001=>100000011111 [1,0,1,0,1,1,0,1,1,0,0,0]=>101011011000=>111110001101=>101100011111 [1,0,1,0,1,1,1,0,0,0,1,0]=>101011100010=>111110110111=>111011011111 [1,0,1,0,1,1,1,0,0,1,0,0]=>101011100100=>111110110001=>100011011111 [1,0,1,0,1,1,1,0,1,0,0,0]=>101011101000=>111110111101=>101111011111 [1,0,1,0,1,1,1,1,0,0,0,0]=>101011110000=>111110100101=>101001011111 [1,0,1,1,0,0,1,0,1,0,1,0]=>101100101010=>111001111111=>111111100111 [1,0,1,1,0,0,1,0,1,1,0,0]=>101100101100=>111001111001=>100111100111 [1,0,1,1,0,0,1,1,0,0,1,0]=>101100110010=>111001100111=>111001100111 [1,0,1,1,0,0,1,1,0,1,0,0]=>101100110100=>111001100001=>100001100111 [1,0,1,1,0,0,1,1,1,0,0,0]=>101100111000=>111001101101=>101101100111 [1,0,1,1,0,1,0,0,1,0,1,0]=>101101001010=>111000011111=>111110000111 [1,0,1,1,0,1,0,0,1,1,0,0]=>101101001100=>111000011001=>100110000111 [1,0,1,1,0,1,0,1,0,0,1,0]=>101101010010=>111000000111=>111000000111 [1,0,1,1,0,1,0,1,0,1,0,0]=>101101010100=>111000000001=>100000000111 [1,0,1,1,0,1,0,1,1,0,0,0]=>101101011000=>111000001101=>101100000111 [1,0,1,1,0,1,1,0,0,0,1,0]=>101101100010=>111000110111=>111011000111 [1,0,1,1,0,1,1,0,0,1,0,0]=>101101100100=>111000110001=>100011000111 [1,0,1,1,0,1,1,0,1,0,0,0]=>101101101000=>111000111101=>101111000111 [1,0,1,1,0,1,1,1,0,0,0,0]=>101101110000=>111000100101=>101001000111 [1,0,1,1,1,0,0,0,1,0,1,0]=>101110001010=>111011011111=>111110110111 [1,0,1,1,1,0,0,0,1,1,0,0]=>101110001100=>111011011001=>100110110111 [1,0,1,1,1,0,0,1,0,0,1,0]=>101110010010=>111011000111=>111000110111 [1,0,1,1,1,0,0,1,0,1,0,0]=>101110010100=>111011000001=>100000110111 [1,0,1,1,1,0,0,1,1,0,0,0]=>101110011000=>111011001101=>101100110111 [1,0,1,1,1,0,1,0,0,0,1,0]=>101110100010=>111011110111=>111011110111 [1,0,1,1,1,0,1,0,0,1,0,0]=>101110100100=>111011110001=>100011110111 [1,0,1,1,1,0,1,0,1,0,0,0]=>101110101000=>111011111101=>101111110111 [1,0,1,1,1,0,1,1,0,0,0,0]=>101110110000=>111011100101=>101001110111 [1,0,1,1,1,1,0,0,0,0,1,0]=>101111000010=>111010010111=>111010010111 [1,0,1,1,1,1,0,0,0,1,0,0]=>101111000100=>111010010001=>100010010111 [1,0,1,1,1,1,0,0,1,0,0,0]=>101111001000=>111010011101=>101110010111 [1,0,1,1,1,1,0,1,0,0,0,0]=>101111010000=>111010000101=>101000010111 [1,0,1,1,1,1,1,0,0,0,0,0]=>101111100000=>111010110101=>101011010111 [1,1,0,0,1,0,1,0,1,0,1,0]=>110010101010=>100111111111=>111111111001 [1,1,0,0,1,0,1,0,1,1,0,0]=>110010101100=>100111111001=>100111111001 [1,1,0,0,1,0,1,1,0,0,1,0]=>110010110010=>100111100111=>111001111001 [1,1,0,0,1,0,1,1,0,1,0,0]=>110010110100=>100111100001=>100001111001 [1,1,0,0,1,0,1,1,1,0,0,0]=>110010111000=>100111101101=>101101111001 [1,1,0,0,1,1,0,0,1,0,1,0]=>110011001010=>100110011111=>111110011001 [1,1,0,0,1,1,0,0,1,1,0,0]=>110011001100=>100110011001=>100110011001 [1,1,0,0,1,1,0,1,0,0,1,0]=>110011010010=>100110000111=>111000011001 [1,1,0,0,1,1,0,1,0,1,0,0]=>110011010100=>100110000001=>100000011001 [1,1,0,0,1,1,0,1,1,0,0,0]=>110011011000=>100110001101=>101100011001 [1,1,0,0,1,1,1,0,0,0,1,0]=>110011100010=>100110110111=>111011011001 [1,1,0,0,1,1,1,0,0,1,0,0]=>110011100100=>100110110001=>100011011001 [1,1,0,0,1,1,1,0,1,0,0,0]=>110011101000=>100110111101=>101111011001 [1,1,0,0,1,1,1,1,0,0,0,0]=>110011110000=>100110100101=>101001011001 [1,1,0,1,0,0,1,0,1,0,1,0]=>110100101010=>100001111111=>111111100001 [1,1,0,1,0,0,1,0,1,1,0,0]=>110100101100=>100001111001=>100111100001 [1,1,0,1,0,0,1,1,0,0,1,0]=>110100110010=>100001100111=>111001100001 [1,1,0,1,0,0,1,1,0,1,0,0]=>110100110100=>100001100001=>100001100001 [1,1,0,1,0,0,1,1,1,0,0,0]=>110100111000=>100001101101=>101101100001 [1,1,0,1,0,1,0,0,1,0,1,0]=>110101001010=>100000011111=>111110000001 [1,1,0,1,0,1,0,0,1,1,0,0]=>110101001100=>100000011001=>100110000001 [1,1,0,1,0,1,0,1,0,0,1,0]=>110101010010=>100000000111=>111000000001 [1,1,0,1,0,1,0,1,0,1,0,0]=>110101010100=>100000000001=>100000000001 [1,1,0,1,0,1,0,1,1,0,0,0]=>110101011000=>100000001101=>101100000001 [1,1,0,1,0,1,1,0,0,0,1,0]=>110101100010=>100000110111=>111011000001 [1,1,0,1,0,1,1,0,0,1,0,0]=>110101100100=>100000110001=>100011000001 [1,1,0,1,0,1,1,0,1,0,0,0]=>110101101000=>100000111101=>101111000001 [1,1,0,1,0,1,1,1,0,0,0,0]=>110101110000=>100000100101=>101001000001 [1,1,0,1,1,0,0,0,1,0,1,0]=>110110001010=>100011011111=>111110110001 [1,1,0,1,1,0,0,0,1,1,0,0]=>110110001100=>100011011001=>100110110001 [1,1,0,1,1,0,0,1,0,0,1,0]=>110110010010=>100011000111=>111000110001 [1,1,0,1,1,0,0,1,0,1,0,0]=>110110010100=>100011000001=>100000110001 [1,1,0,1,1,0,0,1,1,0,0,0]=>110110011000=>100011001101=>101100110001 [1,1,0,1,1,0,1,0,0,0,1,0]=>110110100010=>100011110111=>111011110001 [1,1,0,1,1,0,1,0,0,1,0,0]=>110110100100=>100011110001=>100011110001 [1,1,0,1,1,0,1,0,1,0,0,0]=>110110101000=>100011111101=>101111110001 [1,1,0,1,1,0,1,1,0,0,0,0]=>110110110000=>100011100101=>101001110001 [1,1,0,1,1,1,0,0,0,0,1,0]=>110111000010=>100010010111=>111010010001 [1,1,0,1,1,1,0,0,0,1,0,0]=>110111000100=>100010010001=>100010010001 [1,1,0,1,1,1,0,0,1,0,0,0]=>110111001000=>100010011101=>101110010001 [1,1,0,1,1,1,0,1,0,0,0,0]=>110111010000=>100010000101=>101000010001 [1,1,0,1,1,1,1,0,0,0,0,0]=>110111100000=>100010110101=>101011010001 [1,1,1,0,0,0,1,0,1,0,1,0]=>111000101010=>101101111111=>111111101101 [1,1,1,0,0,0,1,0,1,1,0,0]=>111000101100=>101101111001=>100111101101 [1,1,1,0,0,0,1,1,0,0,1,0]=>111000110010=>101101100111=>111001101101 [1,1,1,0,0,0,1,1,0,1,0,0]=>111000110100=>101101100001=>100001101101 [1,1,1,0,0,0,1,1,1,0,0,0]=>111000111000=>101101101101=>101101101101 [1,1,1,0,0,1,0,0,1,0,1,0]=>111001001010=>101100011111=>111110001101 [1,1,1,0,0,1,0,0,1,1,0,0]=>111001001100=>101100011001=>100110001101 [1,1,1,0,0,1,0,1,0,0,1,0]=>111001010010=>101100000111=>111000001101 [1,1,1,0,0,1,0,1,0,1,0,0]=>111001010100=>101100000001=>100000001101 [1,1,1,0,0,1,0,1,1,0,0,0]=>111001011000=>101100001101=>101100001101 [1,1,1,0,0,1,1,0,0,0,1,0]=>111001100010=>101100110111=>111011001101 [1,1,1,0,0,1,1,0,0,1,0,0]=>111001100100=>101100110001=>100011001101 [1,1,1,0,0,1,1,0,1,0,0,0]=>111001101000=>101100111101=>101111001101 [1,1,1,0,0,1,1,1,0,0,0,0]=>111001110000=>101100100101=>101001001101 [1,1,1,0,1,0,0,0,1,0,1,0]=>111010001010=>101111011111=>111110111101 [1,1,1,0,1,0,0,0,1,1,0,0]=>111010001100=>101111011001=>100110111101 [1,1,1,0,1,0,0,1,0,0,1,0]=>111010010010=>101111000111=>111000111101 [1,1,1,0,1,0,0,1,0,1,0,0]=>111010010100=>101111000001=>100000111101 [1,1,1,0,1,0,0,1,1,0,0,0]=>111010011000=>101111001101=>101100111101 [1,1,1,0,1,0,1,0,0,0,1,0]=>111010100010=>101111110111=>111011111101 [1,1,1,0,1,0,1,0,0,1,0,0]=>111010100100=>101111110001=>100011111101 [1,1,1,0,1,0,1,0,1,0,0,0]=>111010101000=>101111111101=>101111111101 [1,1,1,0,1,0,1,1,0,0,0,0]=>111010110000=>101111100101=>101001111101 [1,1,1,0,1,1,0,0,0,0,1,0]=>111011000010=>101110010111=>111010011101 [1,1,1,0,1,1,0,0,0,1,0,0]=>111011000100=>101110010001=>100010011101 [1,1,1,0,1,1,0,0,1,0,0,0]=>111011001000=>101110011101=>101110011101 [1,1,1,0,1,1,0,1,0,0,0,0]=>111011010000=>101110000101=>101000011101 [1,1,1,0,1,1,1,0,0,0,0,0]=>111011100000=>101110110101=>101011011101 [1,1,1,1,0,0,0,0,1,0,1,0]=>111100001010=>101001011111=>111110100101 [1,1,1,1,0,0,0,0,1,1,0,0]=>111100001100=>101001011001=>100110100101 [1,1,1,1,0,0,0,1,0,0,1,0]=>111100010010=>101001000111=>111000100101 [1,1,1,1,0,0,0,1,0,1,0,0]=>111100010100=>101001000001=>100000100101 [1,1,1,1,0,0,0,1,1,0,0,0]=>111100011000=>101001001101=>101100100101 [1,1,1,1,0,0,1,0,0,0,1,0]=>111100100010=>101001110111=>111011100101 [1,1,1,1,0,0,1,0,0,1,0,0]=>111100100100=>101001110001=>100011100101 [1,1,1,1,0,0,1,0,1,0,0,0]=>111100101000=>101001111101=>101111100101 [1,1,1,1,0,0,1,1,0,0,0,0]=>111100110000=>101001100101=>101001100101 [1,1,1,1,0,1,0,0,0,0,1,0]=>111101000010=>101000010111=>111010000101 [1,1,1,1,0,1,0,0,0,1,0,0]=>111101000100=>101000010001=>100010000101 [1,1,1,1,0,1,0,0,1,0,0,0]=>111101001000=>101000011101=>101110000101 [1,1,1,1,0,1,0,1,0,0,0,0]=>111101010000=>101000000101=>101000000101 [1,1,1,1,0,1,1,0,0,0,0,0]=>111101100000=>101000110101=>101011000101 [1,1,1,1,1,0,0,0,0,0,1,0]=>111110000010=>101011010111=>111010110101 [1,1,1,1,1,0,0,0,0,1,0,0]=>111110000100=>101011010001=>100010110101 [1,1,1,1,1,0,0,0,1,0,0,0]=>111110001000=>101011011101=>101110110101 [1,1,1,1,1,0,0,1,0,0,0,0]=>111110010000=>101011000101=>101000110101 [1,1,1,1,1,0,1,0,0,0,0,0]=>111110100000=>101011110101=>101011110101 [1,1,1,1,1,1,0,0,0,0,0,0]=>111111000000=>101010010101=>101010010101
Map
to binary word
Description
Return the Dyck word as binary word.
Map
alternating inverse
Description
Sends a binary word $w_1\cdots w_m$ to the binary word $v_1 \cdots v_m$ with $v_i = w_i$ if $i$ is odd and $v_i = 1 - w_i$ if $i$ is even.
This map is used in [1], see Definitions 3.2 and 5.1.
Map
reverse
Description
Return the reversal of a binary word.