Catalan intervals and uniquely sorted permutations
نویسندگان
چکیده
منابع مشابه
Sorted and or sortable permutations
In his Ph D thesis Julian West studied in depth a map that acts on permutations of the symmetric group Sn by partially sorting them through a stack The main motivation of this paper is to characterize and count the permutations of Sn which we call sorted permutations This is equivalent to counting preorders of increasing binary trees We rst nd a local characterization of sorted permutations The...
متن کاملOn uniquely k-determined permutations
Motivated by a new point of view to study occurrences of consecutive patterns in permutations, we introduce the notion of uniquely k-determined permutations. We give two criteria for a permutation to be uniquely k-determined: one in terms of the distance between two consecutive elements in a permutation, and the other one in terms of directed hamiltonian paths in the certain graphs called path-...
متن کاملFrom Motzkin to Catalan permutations
For every integer j¿1, we de ne a class of permutations in terms of certain forbidden subsequences. For j = 1, the corresponding permutations are counted by the Motzkin numbers, and for j =∞ (de ned in the text), they are counted by the Catalan numbers. Each value of j¿ 1 gives rise to a counting sequence that lies between the Motzkin and the Catalan numbers. We compute the generating function ...
متن کاملPermutations, Pattern Avoidance, and the Catalan Triangle
In the study of various objects indexed by permutations, a natural notion of minimal excluded structure, now known as a permutation pattern, has emerged and found diverse applications. One of the earliest results from the study of permutation pattern avoidance in enumerative combinatorics is that the Catalan numbers cn count the permutations of size n that avoid any fixed pattern of size three....
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: Journal of Combinatorial Theory, Series A
سال: 2020
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2020.105250