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Symmetric fair cake-cutting is a variant of the fair cake-cutting problem, in which fairness is applied not only to the final outcome, but also to the assignment of roles in the division procedure. As an example, consider a birthday cake that has to be divided between two children with different tastes, such that each child feels that his/her ...
An equitable cake allocation cannot be found using a finite protocol in the Robertson–Webb query model, even for 2 agents. [8] Moreover, for any ε > 0: A connected ε-equitable cake-cutting requires at least Ω(log ε −1) queries. [9] For 2 agents, an O(log ε −1) protocol exists. [5]
The cake number is so-called because one may imagine each partition of the cube by a plane as a slice made by a knife through a cube-shaped cake. It is the 3D analogue of the lazy caterer's sequence. The values of C n for n = 0, 1, 2, ... are given by 1, 2, 4, 8, 15, 26, 42, 64, 93, 130, 176, 232, ... (sequence A000125 in the OEIS).
Fair cake-cutting is a kind of fair division problem. The problem involves a heterogeneous resource, such as a cake with different toppings, that is assumed to be divisible – it is possible to cut arbitrarily small pieces of it without destroying their value. The resource has to be divided among several partners who have different preferences ...
In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter (unlike permutations).For example, given three fruits, say an apple, an orange and a pear, there are three combinations of two that can be drawn from this set: an apple and a pear; an apple and an orange; or a pear and an orange.
Perfect division – the number of pieces equals the number of agents: the cake should be partitioned into n pieces, and all agents agrees that all pieces have equal values. ε {\displaystyle \varepsilon } -near-exact division , for any constant ε > 0 {\displaystyle \varepsilon >0} , the agents may disagree on the pieces values, but the ...
The number associated in the combinatorial number system of degree k to a k-combination C is the number of k-combinations strictly less than C in the given ordering. This number can be computed from C = { c k , ..., c 2 , c 1 } with c k > ... > c 2 > c 1 as follows.
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures.It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics and from evolutionary biology to computer science.