In this paper, we shall construct a bijection between rook placements on double staircases (introduced by Josuat-Vergès in 2017) and increasing binary trees. We introduce two subclasses of staircases, which call left right-aligned placements. show that their enumeration, while keeping track certain statistic, gives the $\gamma$-vectors Eulerian polynomials. conclude with discussion different fi...

The problem of finding a longest increasing subsequence (LIS) is a well known task in sequence processing. There are many variants of the basic task. We discuss a recently introduced variant of LIS, a minimal height longest increasing subsequence problem and propose a new algorithm for it, which improves its time complexity. Moreover, we define a family of similar problems and introduce algorit...

Let Ln be the length of the longest increasing subsequence of a random permutation of the numbers 1, . . . , n, for the uniform distribution on the set of permutations. We discuss the “hydrodynamical approach” to the analysis of the limit behavior, which probably started with Hammersley (1972), and was subsequently further developed by several authors. We also give two proofs of an exact (non-a...

Two-dimensional Lorentzian geometry has recently found application in some models of nonrelativistic systems, most profitably for the process of boarding an aeroplane. The duration of the boarding process is assumed to be a result of passengers standing in the isle and blocking each others’ way. According to this model, the expected boarding time is equal to the length of the longest timelike g...

New algorithm for finding longest increasing subsequence is discussed. This algorithm is based on the ideas of idempotent mathematic and uses Max-Plus idempotent semiring. Problem of finding longest increasing subsequence is reformulated in a matrix form and solved with linear algebra.

the purpose of this research was to assess the influence of several orchard systems involving trees trained to different leader numbers on growth, cropping, and fruit quality of two apple cultivars. the study was conducted during 1994-2007 at the fruit experimental station in samotwór, next to wrocław (south-western poland). one-year-old trees of ‘elstar’ and ‘jonagold’ cultivars on the m.9 roo...

This paper deals with statistics concerning distances between randomly chosen nodes in varieties of increasing trees. Increasing trees are labelled rooted trees where labels along any branch from the root go in increasing order. Many important tree families that have applications in computer science or are used as probabilistic models in various applications, like recursive trees, heap-ordered ...