The combinatorial game Chomp was studied and some computer-proved results on the P-positions and the values of the Sprague-Grundy function are listed. In particular, a formula was proved for a...
My research has been focused on Computer-Assisted and Computer-Generated Mathematics. The emergence of powerful mathematical computing environments, growing availability of correspondingly powerful...
Conducting research on robot mapping and self-localization. The goal of the NSF-supported project is to determine a mobile robot’s position and map its surrounding area by processing information on...
Goncarov-Type Polynomials and Applications in Combinatorics (2009)
Key words and phrases. Goncarov Polynomial, parking functions, lattice path, q-analog Mathematics Subject Classification. In this paper we extend the work of [1] to study combinatorial problems via...
Two-boundary lattice paths and parking functions (2009)
Key words and phrases. Lattice path, parking function, area and sum enumerators,
Stavros Garoufalidis, Xinyu Sun
Abstract. We introduce a new algorithm to find recursions of proper hypergeometric multisums. Our algorithm treats one summation variable at a time, and provides rational certificates along the way....
The p-adic valuations of sequences counting alternating sign matrices (2009)
The p-adic valuations of a sequence of integers T(n) counting alternating sign matrices is examined for p=2 and p=3. Symmetry properties of their graphs produce a new proof of the result that...
A new algorithm for the recursion of multisums with improved universal denominator (2008)
Garoufalidis, Stavros, Sun, Xinyu
The purpose of the paper is two introduce two new algorithms. The first one computes a linear recursion of proper hypergeometric multisums, by treating one summation variable at a time, and provides...
We present a binary tree that describes the 2-adic valuation of a sequence of coefficients arising from the evaluation of a rational integral.
for all n ≥ 1. Two conjectures were proposed on the game by Fraenkel [7]. (2008)
Abstract. The N-heap Wythoff’s game is a two-player impartial game with N piles of tokens of sizes A1,..., AN, A1 ≤ · · · ≤ AN. Players take turns removing any number of tokens from a single...
THE C-POLYNOMIAL OF A KNOT (2008)
Stavros Garoufalidis, Xinyu Sun
Abstract. In an earlier paper the first author defined a non-commutative A-polynomial for knots in 3space, using the colored Jones function. The idea is that the colored Jones function of a knot...
Stavros Garoufalidis, Xinyu Sun
Abstract. The purpose of the paper is two-fold: to introduce a multivariable creative telescoping method, and to apply it in a problem of Quantum Topology: namely the computation of the...
Two-boundary lattice paths and parking functions (2008)
Key words and phrases. Lattice path, parking function, area and sum enumerators,
The non-commutative $A$-polynomial of twist knots (2008)
Garoufalidis, Stavros, Sun, Xinyu
The purpose of the paper is two-fold: to introduce a multivariable creative telescoping method, and to apply it in a problem of Quantum Topology: namely the computation of the non-commutative...
Geometric Robot Mapping (2008)
Rolf Lakaemper, Longin Jan Latecki, Xinyu Sun, Diedrich Wolter
Abstract. The purpose of this paper is to present a technique to create a global map of a robot’s surrounding by converting the raw data acquired from a scanning sensor to a compact map composed of...
Lattice and Schroder paths with periodic boundaries (2007)
Kung, Joseph P. S., De Mier, Anna, Sun, Xinyu, Yan, Catherine H.
We consider paths in the plane with $(1,0),$ $(0,1),$ and $(a,b)$-steps that start at the origin, end at height $n,$ and stay to the left of a given non-decreasing right boundary. We show that if the...
Lattice and Schröder paths with periodic boundaries (2007)
Anna De Mier, Xinyu Sun, Catherine Yan
Key words and phrases. Lattice path, Schröder path, parking function, Appell relation,
The controlled growth of GaN nanowires (2006)
Hersee, Stephen D., Sun, Xinyu, Wang, Xin
This paper reports a scalable process for the growth of high-quality GaN nanowires and uniform nanowire arrays in which the position and diameter of each nanowire is precisely controlled. The...
The C-polynomial of a knot (2005)
Garoufalidis, Stavros, Sun, Xinyu
In an earlier paper, the first author introduced the noncommutative $A$-polynomial of a knot. By definition, it is the characteristic polynomial of the colored Jones function of the knot, and its...
Abstract.
New lower bound on the number of ternary square-free words (2004)
A new lower bound on the number of n-letter ternary square-free words is presented: 110 n=42, which improves the previous best result of 65 n=40
New lower bound on the number of ternary square-free words (2004)
A new lower bound on the number of n-letter ternary square-free words is presented: 110 n/42, which improves the previous best result of 65 n/40. 1.
Annals of Combinatorics On Fraenkel’s N-Heap Wythoff’s Conjectures (2003)
Abstract. The N-heap Wythoff’s game is a two-player impartial game with N piles of tokens of sizes A1,..., AN, A1 ≤ ·· · ≤ AN. Players take turns removing any number of tokens from a single...
Assessing container operator efficiency with heterogeneous and time-varying production frontiers
Yan, Jia, Sun, Xinyu, Liu, John J.
We build an empirical model under the stochastic frontier framework to assess production efficiencies of container operators from the world's major container ports in the years between 1997 and 2004....