Catalan number application in arrangement

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Find the number of ways in which n '1' and n '2' can be arranged in a row that up to any point in the row numbers of '1' is more than or equal to numbers of '2'.



This is the same question asked by me in August 2017, and the answer was that it is a Catalan number.



Me and my team are trying to prove this result but not able to deduce the result which is the Catalan Number. I just need to prove that the result is the CATALAN NUMBER.




combinatorics




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  • 4




    Dyck words satisfy Catalan recurrence
    – qwr
    Jul 28 at 4:57










  • It might help if you state your definition of a Catalan number.
    – awkward
    Jul 28 at 12:26






  • 1




    Consider each one of you '1' characters a '(' character and each '0' character a ')'. The number of desired sequences becomes the number of correct parenthesis sequences of length 2N, which you can prove is the the Nth catalan number. Correct parenthesis sequences are equivalent to dyck words and you can find the proof for the correspondence on wikipedia. I recommend reading the 5th proof of the formula.
    – ã‚¢ãƒªã‚¢ãƒŠã‚¤
    Jul 29 at 17:53














up vote
1
down vote

favorite
2












Find the number of ways in which n '1' and n '2' can be arranged in a row that up to any point in the row numbers of '1' is more than or equal to numbers of '2'.



This is the same question asked by me in August 2017, and the answer was that it is a Catalan number.



Me and my team are trying to prove this result but not able to deduce the result which is the Catalan Number. I just need to prove that the result is the CATALAN NUMBER.




combinatorics




share|cite|improve this question















  • 4




    Dyck words satisfy Catalan recurrence
    – qwr
    Jul 28 at 4:57










  • It might help if you state your definition of a Catalan number.
    – awkward
    Jul 28 at 12:26






  • 1




    Consider each one of you '1' characters a '(' character and each '0' character a ')'. The number of desired sequences becomes the number of correct parenthesis sequences of length 2N, which you can prove is the the Nth catalan number. Correct parenthesis sequences are equivalent to dyck words and you can find the proof for the correspondence on wikipedia. I recommend reading the 5th proof of the formula.
    – ã‚¢ãƒªã‚¢ãƒŠã‚¤
    Jul 29 at 17:53












up vote
1
down vote

favorite
2









up vote
1
down vote

favorite
2






2





Find the number of ways in which n '1' and n '2' can be arranged in a row that up to any point in the row numbers of '1' is more than or equal to numbers of '2'.



This is the same question asked by me in August 2017, and the answer was that it is a Catalan number.



Me and my team are trying to prove this result but not able to deduce the result which is the Catalan Number. I just need to prove that the result is the CATALAN NUMBER.




combinatorics




share|cite|improve this question











Find the number of ways in which n '1' and n '2' can be arranged in a row that up to any point in the row numbers of '1' is more than or equal to numbers of '2'.



This is the same question asked by me in August 2017, and the answer was that it is a Catalan number.



Me and my team are trying to prove this result but not able to deduce the result which is the Catalan Number. I just need to prove that the result is the CATALAN NUMBER.





combinatorics





share|cite|improve this question










share|cite|improve this question




share|cite|improve this question









asked Jul 28 at 4:51









Samar Imam Zaidi

1,051316




1,051316







  • 4




    Dyck words satisfy Catalan recurrence
    – qwr
    Jul 28 at 4:57










  • It might help if you state your definition of a Catalan number.
    – awkward
    Jul 28 at 12:26






  • 1




    Consider each one of you '1' characters a '(' character and each '0' character a ')'. The number of desired sequences becomes the number of correct parenthesis sequences of length 2N, which you can prove is the the Nth catalan number. Correct parenthesis sequences are equivalent to dyck words and you can find the proof for the correspondence on wikipedia. I recommend reading the 5th proof of the formula.
    – ã‚¢ãƒªã‚¢ãƒŠã‚¤
    Jul 29 at 17:53












  • 4




    Dyck words satisfy Catalan recurrence
    – qwr
    Jul 28 at 4:57










  • It might help if you state your definition of a Catalan number.
    – awkward
    Jul 28 at 12:26






  • 1




    Consider each one of you '1' characters a '(' character and each '0' character a ')'. The number of desired sequences becomes the number of correct parenthesis sequences of length 2N, which you can prove is the the Nth catalan number. Correct parenthesis sequences are equivalent to dyck words and you can find the proof for the correspondence on wikipedia. I recommend reading the 5th proof of the formula.
    – ã‚¢ãƒªã‚¢ãƒŠã‚¤
    Jul 29 at 17:53







4




4




Dyck words satisfy Catalan recurrence
– qwr
Jul 28 at 4:57




Dyck words satisfy Catalan recurrence
– qwr
Jul 28 at 4:57












It might help if you state your definition of a Catalan number.
– awkward
Jul 28 at 12:26




It might help if you state your definition of a Catalan number.
– awkward
Jul 28 at 12:26




1




1




Consider each one of you '1' characters a '(' character and each '0' character a ')'. The number of desired sequences becomes the number of correct parenthesis sequences of length 2N, which you can prove is the the Nth catalan number. Correct parenthesis sequences are equivalent to dyck words and you can find the proof for the correspondence on wikipedia. I recommend reading the 5th proof of the formula.
– ã‚¢ãƒªã‚¢ãƒŠã‚¤
Jul 29 at 17:53




Consider each one of you '1' characters a '(' character and each '0' character a ')'. The number of desired sequences becomes the number of correct parenthesis sequences of length 2N, which you can prove is the the Nth catalan number. Correct parenthesis sequences are equivalent to dyck words and you can find the proof for the correspondence on wikipedia. I recommend reading the 5th proof of the formula.
– ã‚¢ãƒªã‚¢ãƒŠã‚¤
Jul 29 at 17:53















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