Type B Catalan numbers as signed permutations
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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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
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
add a comment |
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
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
combinatorics reference-request catalan-numbers coxeter-groups
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
add a comment |
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
add a comment |
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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