Star factorizations and noncrossing partitions
نویسندگان
چکیده
We develop the relationship between minimal transitive star factorizations and noncrossing partitions. This gives a new combinatorial proof of result by Irving Rattan, specialization Kreweras. It also arises in poset on symmetric group whose definition is motivated Subword Property Bruhat order.
منابع مشابه
On Trees and Noncrossing Partitions
We give a simple and natural proof of (an extension of) the identity P (k, l, n) = P2(k − 1, l − 1, n − 1). The number P (k, l, n) counts noncrossing partitions of {1, 2, . . . , l} into n parts such that no part contains two numbers x and y, 0 < y − x < k. The lower index 2 indicates partitions with no part of size three or more. We use the identity to give quick proofs of the closed formulae ...
متن کاملRational Associahedra and Noncrossing Partitions
Each positive rational number x > 0 can be written uniquely as x = a/(b− a) for coprime positive integers 0 < a < b. We will identify x with the pair (a, b). In this paper we define for each positive rational x > 0 a simplicial complex Ass(x) = Ass(a, b) called the rational associahedron. It is a pure simplicial complex of dimension a − 2, and its maximal faces are counted by the rational Catal...
متن کاملNoncrossing Partitions, Toggles, and Homomesies
We introduce n(n−1)/2 natural involutions (“toggles”) on the set S of noncrossing partitions π of size n, along with certain composite operations obtained by composing these involutions. We show that for many operations T of this kind, a surprisingly large family of functions f on S (including the function that sends π to the number of blocks of π) exhibits the homomesy phenomenon: the average ...
متن کاملSets, Lists and Noncrossing Partitions
Partitions of [n] = {1, 2, . . . , n} into sets of lists are counted by sequence A000262 in the On-Line Encyclopedia of Integer Sequences. They are somewhat less numerous than partitions of [n] into lists of sets, A000670. Here we observe that the former are actually equinumerous with partitions of [n] into lists of noncrossing sets and give a bijective proof. We show too that partitions of [n]...
متن کاملON k-NONCROSSING PARTITIONS
In this paper we prove a duality between k-noncrossing partitions over [n] = {1, . . . , n} and k-noncrossing braids over [n − 1]. This duality is derived directly via (generalized) vacillating tableaux which are in correspondence to tangled-diagrams [6]. We give a combinatorial interpretation of the bijection in terms of the contraction of arcs of tangled-diagrams. Furthermore it induces by re...
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: Discrete Mathematics
سال: 2021
ISSN: ['1872-681X', '0012-365X']
DOI: https://doi.org/10.1016/j.disc.2021.112428