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Journals and Conferences
JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact firstname.lastname@example.org. Mathematical… (More)
The density of a permutation pattern π in a permutation σ is the proportion of subsequences of σ of length |π| that are isomorphic to π. The maximal value of the density is found for several patterns π, and asymptotic upper and lower bounds for the maximal density are found in several other cases. The results are generalised to sets of patterns and the… (More)
We show that no finite protocol (even if unbounded) can guarantee an envy-free division of a cake among three or more players, if each player is to receive a single connected piece.
We present a moving-knife procedure, requiring only 11 cuts, that produces an envy-free allocation of a cake among four players and discuss possible extensions to five players.
Given combinatorial games G and H, define a new game G+H to be the game played by two players who alternately make moves of game G until G is exhausted and then proceed to game H. As usual, the player who has no move (in H) loses. Mistre games are a special case of this construction. We explore the theory of these sequential compounds and determine the… (More)
Gale (1993) posed the question of whether there is necessarily an undominated, envy-free allocation of a pie when it is cut into wedge-shaped pieces or sectors. For two players, we give constructive procedures for obtaining such an allocation, whether the pie is cut into equal-size sectors by a single diameter cut or into two sectors of unequal size. Such… (More)
Control of malaria is vital to the industrial development of the South and other warm regions and the engineer is vital to malaria control. The public must coöperate by understanding and by supporting improvements. Here is a plain educational statement of high value. It views the problems from many practical sides and suggests fundamental considerations.
Let s(n) be the side of the smallest square into which it is possible pack n unit squares. We show that s(10) = 3 + √ 1 2 ≈ 3.707 and that s(11) ≥ 2 + 2 √ 4 5 ≈ 3.789. We also show that an optimal packing of 11 unit squares with orientations limited to 0◦ or 45◦ has side 2+2 √ 8 9 ≈ 3.886. These results prove Martin Gardner’s conjecture that n = 11 is the… (More)
David Gale asked in [8, 1993] whether, when a pie is to be divided among n claimants, it is always possible to find a division that is both envy free and undominated. The pie is cut along n radii and the claimants’ preferences are described by separate measures. We answer Gale’s question in the negative for n = 3 by exhibiting three measures on a pie such… (More)