26 citations
- Bridgewater State UniversityUS1 paper
- Brown UniversityUS1 paper
- École Polytechnique Fédérale de LausanneCH1 paper
- Embry–Riddle Aeronautical UniversityUS1 paper
- Embry-Riddle Aeronautical University Daytona Beach Florida CampusUS1 paper
- Eötvös Loránd UniversityHU1 paper
- Massachusetts Institute of TechnologyUS1 paper
- Motley Fool (United States)US1 paper
- Old Dominion UniversityUS1 paper
- University of Central FloridaUS1 paper
- University of ConnecticutUS1 paper
12 papers
Sums of Quaternion Squares and a Theorem of Watson
Tim Banks, Spencer Hamblen, Tim Sherwin +1
We use a representability theorem of G. L. Watson to examine sums of squares in Quaternion rings with integer coefficients. This allows us to determine a large family of such rings…
Sums of Cubes in Quaternion Rings
Madison Gamble, Spencer Hamblen, Blake Schildhauer +1
We investigate a version of Waring's Problem over quaternion rings, focusing on cubes in quaternion rings with integer coefficients. We determine the global upper and lower bounds…
Sums of squares in Quaternion rings
Anna Cooke, Spencer Hamblen, Sam Whitfield
Lagrange's Four Squares Theorem states that any positive integer can be expressed as the sum of four integer squares. We investigate the analogous question over Quaternion rings, f…
Local arboreal representations
Jacqueline Anderson, Spencer Hamblen, Bjorn Poonen +1
Let be a field complete with respect to a discrete valuation of residue characteristic . Let be a separable polynomial of the form Given $a \…
R.E. Axiomatization of Conditional Independence
Pavel Naumov, Brittany Nicholls
The paper investigates properties of the conditional independence relation between pieces of information. This relation is also known in the database theory as embedded multivalued…
Epistemic Logic for Communication Chains
Jeffrey Kane, Pavel Naumov
The paper considers epistemic properties of linear communication chains. It describes a sound and complete logical system that, in addition to the standard axioms of S5 in a multi-…