18 citations · 33 across the 14 of their papers we have counts for
13 papers · 1 filter
The genus distribution of cubic graphs and asymptotic number of rooted cubic maps with high genus
Zhicheng Gao
Let be the number of rooted cubic maps with vertices on the orientable surface of genus . We show that the sequence is asymptotically normal wi…
Asymptotic distribution of the number of zeros in random polynomials in a given equivalence class over a finite field
Zhicheng Gao
Hayes equivalence is defined on monic polynomials over a finite field $\fq$ in terms of the prescribed leading coefficients and the residue classes modulo a given monic polynomial…
Improved error bounds for the number of irreducible polynomials and self-reciprocal irreducible monic polynomials with prescribed coefficients over a finite field
Zhicheng Gao
A polynomial is called self-reciprocal (or palindromic) if the sequence of its coefficients is palindromic. In this paper we obtain improved error bounds for the number of irreduci…
Enumeration of self-reciprocal irreducible monic polynomials with prescribed leading coefficients over a finite field
Zhicheng Gao
A polynomial is called self-reciprocal (or palindromic) if the sequence of its coefficients is palindromic. In this paper we enumerate self-reciprocal irreducible monic polynomials…
More models of walks avoiding a quadrant (extended abstract)
Mireille Bousquet-Melou, Michael Wallner
We continue the enumeration of plane lattice paths avoiding the negative quadrant initiated by the first author in [Bousquet-M{é}lou, 2016]. We solve in detail a new case, the king…
Counting irreducible polynomials with prescribed coefficients over a finite field
Zhicheng Gao, Simon Kuttner, Qiang Wang
We continue our study on counting irreducible polynomials over a finite field with prescribed coefficients. We set up a general combinatorial framework using generating functions w…