Type B Catalan numbers as signed permutations












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The Catalan numbers are in bijection with the 123, 132, etc. avoiding permutations in $S_n$. If we move to type B, the type B Catalan numbers is $binom{2n}{n}$, and the permutation group is the hyperoctahedral group of signed permutations $pm[n]$. Is there a natural bijection between the type B Catalan numbers and a choice of elements of the hyperoctahedral group?



Note: Maybe this is clear if someone knows where the type B Catalan number comes from. I would also be appreciative of any (preferably freely available) resources that discuss Catalan numbers of different Coxeter types.










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  • This makes me wonder: What is known about avoidance of $3$-patterns for signed permutations? (That said, there are likely several ways to interpret this question.)
    – darij grinberg
    Nov 29 at 21:24
















1














The Catalan numbers are in bijection with the 123, 132, etc. avoiding permutations in $S_n$. If we move to type B, the type B Catalan numbers is $binom{2n}{n}$, and the permutation group is the hyperoctahedral group of signed permutations $pm[n]$. Is there a natural bijection between the type B Catalan numbers and a choice of elements of the hyperoctahedral group?



Note: Maybe this is clear if someone knows where the type B Catalan number comes from. I would also be appreciative of any (preferably freely available) resources that discuss Catalan numbers of different Coxeter types.










share|cite|improve this question






















  • This makes me wonder: What is known about avoidance of $3$-patterns for signed permutations? (That said, there are likely several ways to interpret this question.)
    – darij grinberg
    Nov 29 at 21:24














1












1








1







The Catalan numbers are in bijection with the 123, 132, etc. avoiding permutations in $S_n$. If we move to type B, the type B Catalan numbers is $binom{2n}{n}$, and the permutation group is the hyperoctahedral group of signed permutations $pm[n]$. Is there a natural bijection between the type B Catalan numbers and a choice of elements of the hyperoctahedral group?



Note: Maybe this is clear if someone knows where the type B Catalan number comes from. I would also be appreciative of any (preferably freely available) resources that discuss Catalan numbers of different Coxeter types.










share|cite|improve this question













The Catalan numbers are in bijection with the 123, 132, etc. avoiding permutations in $S_n$. If we move to type B, the type B Catalan numbers is $binom{2n}{n}$, and the permutation group is the hyperoctahedral group of signed permutations $pm[n]$. Is there a natural bijection between the type B Catalan numbers and a choice of elements of the hyperoctahedral group?



Note: Maybe this is clear if someone knows where the type B Catalan number comes from. I would also be appreciative of any (preferably freely available) resources that discuss Catalan numbers of different Coxeter types.







combinatorics reference-request catalan-numbers coxeter-groups






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asked Nov 29 at 18:54









Cyclicduck

311110




311110












  • This makes me wonder: What is known about avoidance of $3$-patterns for signed permutations? (That said, there are likely several ways to interpret this question.)
    – darij grinberg
    Nov 29 at 21:24


















  • This makes me wonder: What is known about avoidance of $3$-patterns for signed permutations? (That said, there are likely several ways to interpret this question.)
    – darij grinberg
    Nov 29 at 21:24
















This makes me wonder: What is known about avoidance of $3$-patterns for signed permutations? (That said, there are likely several ways to interpret this question.)
– darij grinberg
Nov 29 at 21:24




This makes me wonder: What is known about avoidance of $3$-patterns for signed permutations? (That said, there are likely several ways to interpret this question.)
– darij grinberg
Nov 29 at 21:24















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