1 citations · 4 across the 8 of their papers we have counts for
9 papers
The Ideal of Vanishing Polynomials and the Ring of Polynomial Functions
Matvey Borodin, Ethan Liu, Justin Zhang
Vanishing polynomials are polynomials over a ring which output for all elements in the ring. In this paper, we study the ideal of vanishing polynomials over specific types of r…
Results on Vanishing Polynomials and Polynomial Root Counting
Matvey Borodin, Ethan Liu, Justin Zhang
We study the set of algebraic objects known as vanishing polynomials (the set of polynomials that annihilate all elements of a ring) over general commutative rings with identity. T…
Sequences of the Stable Matching Problem
Matvey Borodin, Eric Chen, Aidan Duncan +8
In this paper, we begin by discussing different types of preference profiles related to the stable marriage problem. We then introduce the concept of soulmates, which are a man and…
The Stable Matching Problem and Sudoku
Matvey Borodin, Eric Chen, Aidan Duncan +8
Are you having trouble getting married? These days, there are lots of products on the market for dating, from apps to websites and matchmakers, but we know a simpler way! That's ri…
From Unequal Chance to a Coin Game Dance: Variants of Penney's Game
Isha Agarwal, Matvey Borodin, Aidan Duncan +7
We introduce and analyze several variations of Penney's game aimed to find a more equitable game.
The No-Flippancy Game
Isha Agarwal, Matvey Borodin, Aidan Duncan +7
We analyze a coin-based game with two players where, before starting the game, each player selects a string of length comprised of coin tosses. They alternate turns, choosing t…
It's Common Knowledge
Matvey Borodin, Aidan Duncan, Joshua Guo +7
We discuss some old common knowledge puzzles and introduce a lot of new common knowledge puzzles.
Variants of Base 3 over 2
Matvey Borodin, Hannah Han, Kaylee Ji +8
We discuss two different systems of number representations that both can be called 'base 3/2'. We explain how they are connected. Unlike classical fractional extension, these two s…
Chip-Firing and Fractional Bases
Matvey Borodin, Hannah Han, Kaylee Ji +8
We study a particular chip-firing process on an infinite path graph. At any time when there are at least chips at a vertex, chips fire to the left and chips fire to t…