Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: It is known that the normalized volume of standard hypersimplices (defined as some slices of the unit hypercube) are the Eulerian numbers. More generally, a recent conjecture of Stanley relates the Ehrhart series of hypersimplices with descents and excedences in permutations. This conjecture was proved by Nan Li, who also gave a generalization to colored permutations. In this article,  give another generalization to colored permutations, using the flag statistics introduced by Foata and Han.  obtain in particular a new proof of Stanley’s conjecture, and some combinatorial identities relating pairs of Eulerian statistics on colored permutations.
['Guo-Niu Han', 'Matthieu Josuat-Vergès']
I am writing a research paper on a idea Flag Statistics from the Ehrhart $h^∗$-Polynomial of Multi-Hypersimplices
[{"from": "human", "value": "I am writing a research paper on a idea Flag Statistics from the Ehrhart $h^\u2217$-Polynomial of Multi-Hypersimplices"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: It is known that the normalized volume of standard hypersimplices\u00a0(defined as some slices of the unit hypercube) are the Eulerian numbers. More\u00a0generally, a recent conjecture of Stanley relates the Ehrhart series of hypersimplices\u00a0with descents and excedences in permutations. This conjecture was proved by Nan\u00a0Li, who also gave a generalization to colored permutations. In this article,  give\u00a0another generalization to colored permutations, using the flag statistics introduced\u00a0by Foata and Han.  obtain in particular a new proof of Stanley\u2019s conjecture,\u00a0and some combinatorial identities relating pairs of Eulerian statistics on colored\u00a0permutations."}]