G. Xin

works on

academic career 1 biography 1 combinatorics 1 history of mathematics 1 tribute 1

From the 1 of 5 linked papers with an AI index.

collaborators

5 papers

math.HO2026

A memorial tribute: Adriano Garsia (1928--2024)

Hélène Barcelo, HÃ©lÃ¨ne Barcelo, FranÃ§ois Bergeron +18

The paper is a biographical tribute honoring the life and career of mathematician Adriano Garsia, outlining his personal background, education, and academic positions.

math.CO2026

Constructing explicit Sperner chain decompositions for $L (3, n)$ and $L (4, n)$ via Greedy Algorithms and chain tableaux

Guoce Xin, Yueming Zhong

Let $L (m, n)$ denote Young's lattice, consisting of all partitions whose Young diagrams are contained within an $m \times n$ rectangle. It is a classical result that the partially or…

math.CO2025

On Frobenius Numbers of Shifted Power Sequences

Feihu Liu, Guoce Xin

We resolve the open problem of characterizing the Frobenius number $g (A)$ for shifted square sequences $A = (a, a + 1^{2}, \dots, a + k^{2})$ , confirming a conjecture of Einstein et al. (…

math.NT2025

On the Frobenius Number and Genus of a Collection of Semigroups Generalizing Repunit Numerical Semigroups

Feihu Liu, Guoce Xin, Suting Ye +1

Let $A = (a_{1}, a_{2}, \dots, a_{n})$ be a sequence of relative prime positive integers with $a_{i} \geq 2$ . The Frobenius number $F (A)$ is the largest integer not belonging to the numerica…

math.CO2025

Fast Evaluation of Generalized Todd Polynomials: Applications to MacMahon's Partition Analysis and Integer Programming

Guoce Xin, Yingrui Zhang, ZiHao Zhang

The Todd polynomials, denoted as $t d_{k} (b_{1}, b_{2}, \dots, b_{m})$ , are characterised by their generating functions: $k \geq 0 \sum t d_{k} s^{k} = i = 1 \prod m \frac{b _{i} s}{e ^{b_{i} s} - 1} .$ …

A memorial tribute: Adriano Garsia (1928--2024)

Constructing explicit Sperner chain decompositions for L(3,n) and L(4,n) via Greedy Algorithms and chain tableaux

On Frobenius Numbers of Shifted Power Sequences

On the Frobenius Number and Genus of a Collection of Semigroups Generalizing Repunit Numerical Semigroups

Fast Evaluation of Generalized Todd Polynomials: Applications to MacMahon's Partition Analysis and Integer Programming

Constructing explicit Sperner chain decompositions for $L (3, n)$ and $L (4, n)$ via Greedy Algorithms and chain tableaux