Some factorisations counted by Catalan numbers
نویسندگان
چکیده
منابع مشابه
Surprising Symmetries in Objects Counted by Catalan Numbers
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
متن کاملA self-dual poset on objects counted by the Catalan numbers and a type-B analogue
We introduce two partially ordered sets, P n and P B n , of the same cardinalities as the type-A and type-B noncrossing partition lattices. The ground sets of P n and P B n are subsets of the symmetric and the hyperoctahedral groups, consisting of permutations which avoid certain patterns. The order relation is given by (strict) containment of the descent sets. In each case, by means of an expl...
متن کاملSome Properties of the Fuss–catalan Numbers
In the paper, the authors express the Fuss–Catalan numbers as several forms in terms of the Catalan–Qi function, find some analytic properties, including the monotonicity, logarithmic convexity, complete monotonicity, and minimality, of the Fuss–Catalan numbers, and derive a double inequality for bounding the Fuss–Catalan numbers.
متن کاملObjects Counted by the Central Delannoy Numbers
The central Delannoy numbers, (dn)n≥0 = 1, 3, 13, 63, 321, 1683, 8989, 48639, . . . (A001850 of The On-Line Encyclopedia of Integer Sequences) will be defined so that dn counts the lattice paths running from (0, 0) to (n, n) that use the steps (1, 0), (0, 1), and (1, 1). In a recreational spirit we give a collection of 29 configurations that these numbers count.
متن کاملCatalan numbers
Catalan numbers appear in many places throughout mathematics, and are a fairly frequent subject for articles in this magazine. Indeed, a very nice introduction to their properties was given in this magazine by Vun and Belcher [3], and a historical account of their discovery in Chinese mathematics (before Catalan!) has also appeared in a recent article by Larcombe [1]. The article by Vun and Bel...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2006
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2005.04.004