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Dual Chow polynomials of matroids and posets
Giovanni Caiolo, Luis Ferroni, Elena Hoster
We introduce and study dual Chow functions associated to kernels in incidence algebras of weakly ranked posets. Given a kernel, its dual Chow function is defined as the Chow functi…
Extending the ab-index
Elena Hoster, Christian Stump, Lorenzo Vecchi
We prove for finite, graded, bounded posets, that the Poincaré-extended ab-index is obtained from the ab-index via the omega-transformation. This proves a conjecture by Dorpalen-Ba…
Chow polynomials of simplicial posets with positive -vector are real-rooted
Elena Hoster, Christian Stump
We prove that a finite graded simplicial poset with a top element added has real-rooted Chow and augmented Chow polynomials whenever it has a positive -vector. This class of pos…
The Chow and augmented Chow polynomials of uniform matroids
Elena Hoster
We provide explicit combinatorial formulas for the Chow polynomial and for the augmented Chow polynomial of uniform matroids, thereby proving a conjecture by Ferroni. These formula…
The coarse flag Hilbert-Poincaré series of the braid arrangement
Elena Hoster, Christian Stump
The paper concerns the coarse flag Hilbert-Poincaré series of Maglione-Voll in the case of the braid arrangement associated to the symmetric group. We explicitly construct a compan…