On Operators on Polynomials Preserving Real-Rootedness and the Neggers-Stanley Conjecture

On the Neggers–Stanley Conjecture and th

On the Neggers–Stanley Conjecture and the Eulerian Polynomials

✍ Vesselin Gasharov 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 387 KB

We prove combinatorially that the W-polynomials of naturally labeled graded posets of rank 1 or 2 (an antichain has rank 0) are unimodal, thus providing further supporting evidence for the Neggers Stanley conjecture. For such posets we also obtain a combinatorial proof that the W-polynomials are sym