Surprising Symmetries in Objects Counted by Catalan Numbers
نویسنده
چکیده
We prove that the total number Sn,132(q) of copies of the pattern q in all 132avoiding permutations of length n is the same for q = 231, q = 312, or q = 213. We provide a combinatorial proof for this unexpected threefold symmetry. We then significantly generalize this result by proving a large family of non-trivial equalities of the type Sn,132(q) = Sn,132(q ). Dedicated to the memory of Herb Wilf
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ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 19 شماره
صفحات -
تاریخ انتشار 2012