8 citations · 48 across the 76 of their papers we have counts for
33 papers · 1 filter
Ending States of a Special Variant of the Chip-Firing Algorithm
Tanya Khovanova, Rich Wang
We investigate a special variant of chip-firing, in which we consider an infinite set of rooms on a number line, some of which are occupied by violinists. In a move, we take two vi…
Combinatorial Aspects of the Card Game War
Tanya Khovanova, Atharva Pathak
This paper studies a single-suit version of the card game War on a finite deck of cards. There are varying methods of how players put the cards that they win back into their hands,…
The Penney's Game with Group Action
Tanya Khovanova, Sean Li
Consider equipping an alphabet with a group action that partitions the set of words into equivalence classes which we call patterns. We answer standard questions for…
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…
3-Symmetric Graphs
Sebastian Jeon, Tanya Khovanova
An intuitive property of a random graph is that its subgraphs should also appear randomly distributed. We consider graphs whose subgraph densities exactly match their expected valu…
The 5-Way Scale
Tanya Khovanova, Joshua Lee
In this paper, we discuss coin-weighing problems that use a 5-way scale which has five different possible outcomes: MUCH LESS, LESS, EQUAL, MORE, and MUCH MORE. The 5-way scale pro…
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…
Limit Densities of Patterns in Permutation Inflations
Tanya Khovanova, Eric Zhang
Call a permutation -inflatable if the sequence of its tensor products with uniform random permutations of increasing lengths has uniform -point pattern densities. Previous wo…
PRIMES STEP Plays Games
Pratik Alladi, Neel Bhalla, Tanya Khovanova +7
A group of students in 7-9 grades are inventing combinatorial impartial games. The games are played on graphs, piles, and grids. We found winning positions, optimal strategies, and…
On Variations of Nim and Chomp
June Ahn, Benjamin Chen, Richard Chen +8
We study two variations of Nim and Chomp which we call Monotonic Nim and Diet Chomp. In Monotonic Nim the moves are the same as in Nim, but the positions are non-decreasing numbers…
Coins that Change Their Weights
Tanya Khovanova, Konstantin Knop
As in many coin puzzles, we have several identical-looking coins, with one of them fake and the rest real. The real coins weigh the same. Our fake coin is special in that it can ch…
Discreet Coin Weighings and the Sorting Strategy
Tanya Khovanova, Rafael M. Saavedra
In 2007, Alexander Shapovalov posed an old twist on the classical coin weighing problem by asking for strategies that manage to conceal the identities of specific coins while provi…
Alternator Coins
Benjamin Chen, Ezra Erives, Leon Fan +9
We introduce a new type of coin: \textit{the alternator}. The alternator can pretend to be either a real or a fake coin (which is lighter than a real one). Each time it is put on a…
Chocolate Numbers
Caleb Ji, Tanya Khovanova, Robin Park +1
In this paper, we consider a game played on a rectangular gridded chocolate bar. Each move, a player breaks the bar along a grid line. Each move after that consists of…
On the Structure of nil-Temperley-Lieb Algebras of type A
Niket Gowravaram, Tanya Khovanova
We investigate nil-Temperley-Lieb algebras of type A. We give a general description of the structure of monomials formed by the generators. We also show that the dimensions of thes…
P-positions in Modular Extensions to Nim
Tanya Khovanova, Karan Sarkar
In this paper, we consider a modular extension to the game of Nim, which we call -Modular Nim, and explore its optimal strategy. In -Modular Nim, a player can either make a s…
There are no Coincidences
Tanya Khovanova
This paper is inspired by a seqfan post by Jeremy Gardiner. The post listed nine sequences with similar parities. In this paper I prove that the similarities are not a coincidence…
Nim Fractals
Tanya Khovanova, Joshua Xiong
We enumerate P-positions in the game of Nim in two different ways. In one series of sequences we enumerate them by the maximum number of counters in a pile. In another series of se…
Fission of Halving Edges Graphs
Tanya Khovanova, Dai Yang
In this paper we discuss an operation on halving edges graph that we call fission. Fission replaces each point in a given configuration with a small cluster of k points. The operat…
Convex geometric (k+2)-quasiplanar representations of semi-bar k-visibility graphs
Jesse Geneson, Tanya Khovanova, Jonathan Tidor
We examine semi-bar visibility graphs in the plane and on a cylinder in which sightlines can pass through k objects. We show every semi-bar k-visibility graph has a (k+2)-quasiplan…
Skyscraper Numbers
Tanya Khovanova, Joel Brewster Lewis
We introduce numbers depending on three parameters which we call skyscraper numbers. We discuss properties of these numbers and their relationship with Stirling numbers of the firs…
Connected Components of Underlying Graphs of Halving Lines
Tanya Khovanova, Dai Yang
In this paper we discuss the connected components of underlying graphs of halving lines' configurations. We show how to create a configuration whose underlying graph is the union o…
Halving Lines and Their Underlying Graphs
Tanya Khovanova, Dai Yang
In this paper we study underlying graphs corresponding to a set of halving lines. We establish many properties of such graphs. In addition, we tighten the upper bound for the numbe…
Saturated Domino Coverings
Andrew Buchanan, Tanya Khovanova, Alex Ryba
A domino covering of a board is saturated if no domino is redundant. We introduce the concept of a fragment tiling and show that a minimal fragment tiling always corresponds to a m…