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Chip-firing is a combinatorial game on a graph, in which chips are placed and dispersed among its vertices until a stable configuration is achieved. We specifically study a chip-firing variant on an infinite, rooted, directed$k$ -ary tree where we place$k^n$chips labeled$0,1,\\dots, k^n-1$on the root for some nonnegative integer$n$ , and we say a vertex$v$can fire if it has at least$k$chips. When a vertex fires, we select$k$labeled chips and send the$i$ th smallest chip among them to its$i$ th leftmost child. A stable configuration is reached when no vertex can fire. In this paper, we focus on stable configurations resulting from specific firing strategies based on permutations of$1, 2, \\dots, n$ . We then express the stable configuration as a permutation of$0,1, 2, \\dots, k^n-1$and explore its properties, such as the number of inversions and descents. 20 pages, 4 figures, 1 table, v4: final version

The media system in China is not totally different from the systems in all other countries in the world. This paper will explain the nature of the media system in China and its internal mechanics from a Chinese perspective. The media system in China is a combination of different media philosophies and the result of the long history of Chinese civilisation. In this system, the Chinese Communist Party, government, private enterprises, media professionals, public individuals and Chinese culture play different roles and provide different forces from different directions and in different fashions. By analysing each force and their interaction inside the media system in China, this paper elucidates the mechanics of the media system in China and attempts to explore the possibility of using these mechanics as a new model to explain media phenomena in China.

Chip-firing on a directed graph is a game in which chips, a discrete commodity, are placed on the vertices of the graph and are transferred between vertices. In this paper, we study a chip-firing game on the Hasse diagram of the lattice of nonnegative integer points on the plane, where we start with \\(2^n\\) chips at the origin. When we fire a vertex \\(v\\), we send one chip to each out-neighbor. We fire until we reach a stable configuration, a distribution of chips where no vertex can fire. We study the intermediate firing configuration: a table that assigns to each vertex the total number of chips that pass through it. We prove that the nonzero entries of the stable configuration correspond to the odd entries of the intermediate configuration. The intermediate configuration consists of three parts: the top triangle, the midsection, and the bottom triangle. We describe properties of each part. We study properties of each row and the number of rows of the intermediate configuration. We also explore properties of the difference tables, which are tables of first differences of each row of the intermediate firing configuration.

Chip-firing is a combinatorial game on a graph, in which chips are placed and dispersed among its vertices until a stable configuration is achieved. We specifically study a chip-firing variant on an infinite, rooted, directed \\(k\\)-ary tree where we place \\(k^n\\) chips labeled \\(0,1, k^n-1\\) on the root for some nonnegative integer \\(n\\), and we say a vertex \\(v\\) can fire if it has at least \\(k\\) chips. When a vertex fires, we select \\(k\\) labeled chips and send the \\(i\\)th smallest chip among them to its \\(i\\)th leftmost child. A stable configuration is reached when no vertex can fire. In this paper, we focus on stable configurations resulting from specific firing strategies based on permutations of \\(1, 2, n\\). We then express the stable configuration as a permutation of \\(0,1, 2, k^n-1\\) and explore its properties, such as the number of inversions and descents.

Chip-firing is a combinatorial game played on a graph, in which chips are placed and dispersed on the vertices until a stable configuration is achieved. We study a chip-firing variant on an infinite, rooted directed \\(k\\)-ary tree, where we place \\(k^n\\) chips labeled \\(1,2,3, k^n\\) on the root for some nonnegative integer \\(n\\). A vertex \\(v\\) can fire if it has at least \\(k\\) chips; when it fires, \\(k\\) chips are selected, and the chip with the \\(i\\)th smallest label is sent to the \\(i\\)th leftmost child of \\(v\\). A stable configuration is reached when no vertices can fire. In this paper, we prove numerous properties of the stable configuration, such as that chips land on vertices in ranges and the lengths of those ranges. We also describe where each chip can land. This helps us describe possible stable configurations of the game.

Chip-firing is a combinatorial game played on a graph in which we place and disperse chips on vertices until a stable state is reached. We study a chip-firing variant played on an infinite rooted directed \\(k\\)-ary tree, where we place \\(k^\\) chips on the root for some positive integer \\(\\), and we say a vertex \\(v\\) can fire if it has at least \\(k\\) chips. A vertex fires by dispersing one chip to each out-neighbor. Once every vertex has less than \\(k\\) chips, we reach a stable configuration since no vertex can fire. We determine the exact number and properties of the possible stable configurations of chips in the setting where chips are distinguishable.

While the anomalous Hall effect can manifest even without an external magnetic field, time reversal symmetry is nonetheless still broken by the internal magnetization of the sample. Recently, it has been shown that certain materials without an inversion center allow for a nonlinear type of anomalous Hall effect whilst retaining time reversal symmetry. The effect may arise from either Berry curvature or through various asymmetric scattering mechanisms. Here, we report the observation of an extremely large c -axis nonlinear anomalous Hall effect in the non-centrosymmetric T d phase of MoTe 2 and WTe 2 without intrinsic magnetic order. We find that the effect is dominated by skew-scattering at higher temperatures combined with another scattering process active at low temperatures. Application of higher bias yields an extremely large Hall ratio of E ⊥ / E ||  = 2.47 and corresponding anomalous Hall conductivity of order 8 × 10 7  S/m. Certain materials without inversion symmetry may allow for a nonlinear anomalous Hall effect with conserved time reversal symmetry. Here, the authors report an extremely large c -axis nonlinear anomalous Hall effect in the non-centrosymmetric T d phase of MoTe 2 and WTe 2 without intrinsic magnetic order that is dominated by extrinsic scattering.