On the symmetry of ascents and descents over 01-fillings of moon polyominoes

Increasing and Decreasing Sequences in Fillings of Moon Polyominoes

We present an adaptation of jeu de taquin and promotion for arbitrary fillings of moon polyominoes. Using this construction we show various symmetry properties of such fillings taking into account the lengths of longest increasing and decreasing chains. In particular, we prove a conjecture of Jakob Jonsson. We also relate our construction to the one recently employed by Christian Krattenthaler, thus generalising his results.

Increasing and Decreasing Sequences of Length Two in 01-Fillings of Moon Polyominoes

We put recent results on the symmetry of the joint distribution of the numbers of crossings and nestings of two edges over matchings, set partitions and linked partitions, in the larger context of the enumeration of increasing and decreasing chains of length 2 in fillings of moon polyominoes.

Maximal increasing sequences in fillings of almost-moon polyominoes

It was proved by Rubey that the number of fillings with zeros and ones of a given moon polyomino that do not contain a northeast chain of size $k$ depends only on the set of columns of the polyomino, but not the shape of the polyomino. Rubey's proof is an adaption of jeu de taquin and promotion for arbitrary fillings of moon polyominoes. In this paper we present a bijective proof for this result by considering fillings of almost-moon polyominoes, which are moon polyominoes after removing one of the rows. Explicitly, we construct a bijection which preserves the size of the largest northeast cha…

矩形与月亮多米诺中的分段线性提升与RSK

Piecewise-linear promotion and RSK in rectangles and moon polyominoes

本研究探讨月亮多米诺与矩形中Schützenberger提升、清空及RSK对应的分段线性/双有理提升，证明链统计量的偏移规律，构建保统计量的Rubey双射版本并验证其交换性，推导相关链多面体类似物的Ehrhart性质。

L-凸多联骨牌与避201上升序列的数值研究

A numerical study of L-convex polyominoes and 201-avoiding ascent sequences

本文研究了L-凸多联骨牌生成函数系数的渐近性态，并猜想出避201上升序列的D-有限代数解，同时展示了相关分析方法以期更广泛应用。

Major Index for 01-Fillings of Moon Polyominoes

We propose a major index statistic on 01-fillings of moon polyominoes which, when specialized to certain shapes, reduces to the major index for permutations and set partitions. We consider the set F(M, s; A) of all 01-fillings of a moon polyomino M with given column sum s whose empty rows are A, and prove that this major index has the same distribution as the number of north-east chains, which are the natural extension of inversions (resp. crossings) for permutations (resp. set partitions). Hence our result generalizes the classical equidistribution results for the permutation statistics inv a…