2020/05/13 by Shishuo Fu, Fu, Shishuo, Guo-Niu Han +3 · 1 citation
Mathematics · Agricultural and Biological Sciences · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Botanical Research and Chemistry
paper · pdf · doi:10.48550/arxiv.2005.06354
The k-arrangements are permutations whose fixed points are k-colored. We prove enumerative results related to statistics and patterns on k-arrangements, confirming several conjectures by Blitvić and Steingrímsson. In particular, one of their conjectures regarding the equdistribution of the number of descents over the derangement form and the permutation form of k-arrangements is strengthened in two interesting ways. Moreover, as one application of the so-called Decrease Value Theorem, we calculate the generating function for a symmetric pair of Eulerian statistics over permutations arising in our study.