We construct an explicit bijection between rigged configurations and rooted planar trees, which we prove is the composition of the the bijection defined by Kerov, Kirillov, and Reshitikhin between rigged configurations and Dyck paths and the bijection between Dyck paths and rooted planar trees defined by the planar code.

We construct a bijection between 231-avoiding permutations and Dyck paths that sends the sum of the major index and the inverse major index of a 231avoiding permutation to the major index of the corresponding Dyck path. Furthermore, we relate this bijection to others and exhibit a bistatistic on 231-avoiding permutations which is related to the q, t-Catalan numbers.

Let integer be any C/C++ unsigned integer type up to 64-bits long. Given a Dyck word the following code returns the next Dyck word of the same size, provided it exists. integer next_dyck_word(integer w) { integer const a = w & -w; integer const b = w + a; integer c = w ^ b; c = (c / a >> 2) + 1; c = ((c * c 1) & 0xaaaaaaaaaaaaaaaa) | b; return c; }

Arvoles lloran por lluvia y montañas por aire Ansí lloran mis ojos por ti querido amante Ladino folk song Abstract. Since ordered trees and Dyck paths are equinumerous, so are ordered forests and grand-Dyck paths that start with an upwards step.

We determine a general formula to compute the number of saturated chains in Dyck lattices, and we apply it to find the number of saturated chains of length 2 and 3. We also compute what we call the Hasse index (of order 2 and 3) of Dyck lattices, which is the ratio between the total number of saturated chains (of length 2 and 3) and the cardinality of the underlying poset.

Let D2n be a Dyck path chosen uniformly in the set of Dyck paths with 2n steps. The aim of this note is to show that for any λ > 0 the sequence E(exp(λ(2n) maxD2n)) converges, and therefore is bounded uniformly in n. The uniform bound justifies an assumption used in literature to prove certain estimates of high moments of large random matrices.

Many program analyses need to reason about pairs of matching actions, such as call/return, lock/unlock, or set-field/get-field. The family Dyck languages { D k }, where has kinds parenthesis pairs, can be used model actions balanced parentheses. Consequently, many program-analysis problems formulated Dyck-reachability on edge-labeled digraphs. Interleaved (InterDyck-reachability), denoted by ⊙ ...

Recently, a new definition for a Wigner distribution function for a one-dimensional finite quantum system, in which the position and momentum operators have a finite (multiplicityfree) spectrum, was developed. This distribution function is defined on discrete phase-space (a finite square grid), and can thus be referred to as the Wigner matrix. In the current paper, we compute this Wigner matrix...