The Dubins–Spanier theorems are several theorems in the theory of fair cake-cutting. They were published by Lester Dubins and Edwin Spanier in 1961. Although...

Spanier–Whitehead duality and Alexander–Spanier cohomology, and wrote what was for a long time the standard textbook on algebraic topology (Spanier 1981)...

Together with Gideon E. Schwarz he proved the Dubins–Schwarz theorem. Dubins–Spanier theorems Dubins, L. E. (1957). "On Curves of Minimal Length with...

1963), or bread and butter and ham (Dubins & Spanier 1961). In two dimensions, the theorem is known as the pancake theorem to refer to the flat nature of the...

particular envy-free; see Dubins–Spanier theorems. There exists an envy-free division which is also Pareto efficient; See Weller's theorem. Both proofs work only...

noted by Jerzy Neyman in 1946, and proved as a corollary of the Dubins–Spanier theorems in 1961. The problem in this case is called the exact division...

to the development of the Alexander–Spanier cohomology, Dubins–Spanier theorems and Spanier–Whitehead duality Frank Spitzer (BA, Ph.D.), mathematician...

Pareto-efficient. The RNS was introduced as part of the Dubins–Spanier theorems and used in the proof of Weller's theorem and later results by Ethan Akin. The term...

no agent envies another agent's share). A corollary of the Dubins–Spanier convexity theorem (1961) is that there always exists a "consensus partition"...

The IPS is a convex set and a compact set. This follows from the Dubins–Spanier theorems. With two agents, the IPS is symmetric across the middle point...

moving-knives procedure The Robertson–Webb rotating-knife procedure The Dubins–Spanier moving-knife procedure Peterson, Elisha; Su, Francis Edward (2002)....

Maxsum divisions still exist. This is a corollary of the Dubins–Spanier compactness theorem and it can also be proved using the Radon–Nikodym set. However...

discrete and can be played in turns. It requires O(n2) actions. The Dubins–Spanier Moving-knife procedure is a continuous-time version of Last diminisher...

of the Dubins–Spanier convexity theorem (the existence of a consensus 1/k-division was previously noted by Jerzy Neyman). However, this theorem says nothing...

partners receive more than 1/n. The proof was a corollary to the Dubins–Spanier convexity theorem. This was a purely existential proof based on convexity arguments...

1/n. The existence of such a division is a corollary of the Dubins–Spanier convexity theorem. Moreover, there exists such a division with at most n ( n...