10 citations · 24 across the 16 of their papers we have counts for
22 papers
Finite Cardinalities of Misère Quotients
Simon Rubinstein-Salzedo, Stephen Zhou
We find that partisan misère quotients can have any finite cardinality other than 3, answering a question of Allen. This contrasts with impartial misère quotients, which must have…
Evil Twins in Sums of Wildflowers
Simon Rubinstein-Salzedo, Stephen Zhou
A game is said to have the evil twin property if there exists such that and . We study sums of wildflowers, games of…
RSK-Complete Cycle Decompositions
Agastya Goel, Simon Rubinstein-Salzedo
We characterize the class of cycle decompositions that can achieve all Young tableau shapes (except the trivial ones with a single row or a single column) under the Robinson--Schen…
Inscribed triangles of Jordan curves in
Aryaman Gupta, Simon Rubinstein-Salzedo
Nielsen's theorem states that any triangle can be inscribed in a planar Jordan curve. We prove a generalisation of this theorem, extending to any Jordan curve embedded in $\mat…
Memgames
Urban Larsson, Simon Rubinstein-Salzedo, Aaron N. Siegel
In this article, we study the structure, and in particular the Grundy values, of a family of games known as memgames.
Cyclotomic Coincidences
Carl Pomerance, Simon Rubinstein-Salzedo
In this paper, we show that if and are distinct positive integers and is a nonzero real number with , then except when $\{m,n\}=\{2,6…
Diophantine Tuples over
Nitya Mani, Simon Rubinstein-Salzedo
For an element of a ring , a Diophantine -tuple is an -tuple of elements of such that for all with , is a p…
Stability for Take-Away Games
Simon Rubinstein-Salzedo, Sherry Sarkar
In this paper, we study a family of take-away games called -tag, parametrized by a real number . We show that for any given , there is a half-open interval cont…
Play in Candy Nim
Nitya Mani, Rajiv Nelakanti, Simon Rubinstein-Salzedo +1
Candy Nim is a variant of Nim in which both players aim to take the last candy in a game of Nim, with the added simultaneous secondary goal of taking as many candies as possible. W…
The Asymmetric Colonel Blotto Game
Simon Rubinstein-Salzedo, Yifan Zhu
This paper explores the Nash equilibria of a variant of the Colonel Blotto game, which we call the Asymmetric Colonel Blotto game. In the Colonel Blotto game, two players simultane…
Reduction of dynatomic curves
John R. Doyle, Holly Krieger, Andrew Obus +3
The dynatomic modular curves parametrize polynomial maps together with a point of period . It is known that the dynatomic curves are smooth and irreducible in character…
Could Euler have conjectured the prime number theorem?
Simon Rubinstein-Salzedo
In this article, we investigate how Euler might have been led to conjecture the Prime Number Theorem, based on what he knew. We also speculate on why he did not do so.
Finite ramification for preimage fields of postcritically finite morphisms
Andrew Bridy, Patrick Ingram, Rafe Jones +5
Given a finite endomorphism of a variety defined over the field of fractions of a Dedekind domain, we study the extension $K(φ^{-\infty}(α)) : = \bigcup_{n \geq 1} K(φ^…
Noncrossing partitions, toggles, and homomesies
David Einstein, Miriam Farber, Emily Gunawan +4
We introduce natural involutions ("toggles") on the set of noncrossing partitions of size , along with certain composite operations obtained by composing thes…
Global Fibonacci Nim
Urban Larsson, Simon Rubinstein-Salzedo
Fibonacci nim is a popular impartial combinatorial game, usually played with a single pile of stones. The game is appealing due to its surprising connections with the Fibonacci num…
-Division Points of Hypocycloids
Nitya Mani, Simon Rubinstein-Salzedo
We show that the -division points of all rational hypocycloids are constructible with an unmarked straightedge and compass for all integers , given a pre-drawn hypocycloid. W…
Grundy values of Fibonacci nim
Urban Larsson, Simon Rubinstein-Salzedo
In this article, we investigate the Grundy values of the popular game of Fibonacci nim. The winning strategy, which amounts to understanding positions of Grundy value 0, was known…
Curvature and Concentration of Hamiltonian Monte Carlo in High Dimensions
Susan Holmes, Simon Rubinstein-Salzedo, Christof Seiler
In this article, we analyze Hamiltonian Monte Carlo (HMC) by placing it in the setting of Riemannian geometry using the Jacobi metric, so that each step corresponds to a geodesic o…
Analysis on Surreal Numbers
Simon Rubinstein-Salzedo, Ashvin Swaminathan
The class of surreal numbers, which John Conway discovered while studying combinatorial games, possesses a rich numerical structure and shares many arithmetic and alg…
Period Computations for Covers of Elliptic Curves
Simon Rubinstein-Salzedo
In this article, we construct algebraic equations for a curve C and a map f to an elliptic curve E, with pre-specified branching data. We do this by determining certain relations t…
Covers of Elliptic Curves with Unique, Totally Ramified Branch Points
Simon Rubinstein-Salzedo
A well-known and difficult problem in computational number theory and algebraic geometry is to write down equations for branched covers of algebraic curves with specified monodromy…
Invariants for A4 fields and the Cohen-Lenstra heuristics
Simon Rubinstein-Salzedo
This article discusses deviations from the Cohen-Lenstra heuristics when roots of unity are present. In particular, we propose an explanation for the discrepancy between the observ…