Ayyer, A and Bényi, B (2021) Toppling on permutations with an extra chip. In: Electronic Journal of Combinatorics, 28 (4).
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Abstract
The study of toppling on permutations with an extra labeled chip was initiated by the first author with D. Hathcock and P. Tetali (arXiv:2010.11236), where the extra chip was added in the middle. We extend this to all possible locations p as well as values r of the extra chip and give a complete characterization of permutations which topple to the identity. Further, we classify all permutations which are outcomes of the toppling process in this generality, which we call resultant permutations. Resultant permutations turn out to be certain decomposable permutations. The number of configurations toppling to a given resultant permutation is shown to depend purely on the number of left-to-right maxima (or records) of the permutation to the left of p and the number of right-to-left minima to the right of p. The number of permutations toppling to a given resultant permutation (identity or otherwise) is shown to be the binomial transform of a poly-Bernoulli number of type B. © The authors. Released under the CC BY license (International 4.0).
| Item Type: | Journal Article |
|---|---|
| Publication: | Electronic Journal of Combinatorics |
| Publisher: | Australian National University |
| Additional Information: | The copyright for this article belongs to Australian National University |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 18 Nov 2021 09:27 |
| Last Modified: | 18 Nov 2021 09:27 |
| URI: | http://eprints.iisc.ac.in/id/eprint/70585 |
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