Exact Forbidden Subposet Results using Chain Decompositions of the Cycle
نویسندگان
چکیده
We introduce a method of decomposing the family of intervals along a cyclic permutation into chains to determine the size of the largest family of subsets of [n] not containing one or more given posets as a subposet. De Bonis, Katona and Swanepoel determined the size of the largest butterfly-free family. We strengthen this result by showing that, for certain posets containing the butterfly poset as a subposet, the same bound holds. We also obtain the corresponding LYM-type inequalities.
منابع مشابه
The partition method for poset-free families
Given a finite poset P , let La(n, P ) denote the largest size of a family of subsets of an n-set that does not contain P as a (weak) subposet. We employ a combinatorial method, using partitions of the collection of all full chains of subsets of the nset, to give simpler new proofs of the known asymptotic behavior of La(n, P ), as n → ∞, when P is the r-fork Vr, the four-element N poset N , and...
متن کامل1 2 Ju n 20 11 Set families with a forbidden induced subposet
For each poset H whose Hasse diagram is a tree of height k, we show that the largest size of a family F of subsets of [n] = {1, . . . , n} not containing H as an induced subposet is asymptotic to (k − 1) ( n ⌊n/2⌋ ) . This extends the result of Bukh [4], which in turn generalizes several known results including Sperner’s theorem. 1
متن کاملIntegrated Competitive Pricing and Transshipment Problem for Short Life Cycle Products’ Supply Chain
This paper integrates competitive pricing and network design problems for the short life cycle products. The pricing problem determines selling prices of the products for different life cycle phases in a competitive market, as well as acquisition management of returned products. Besides, the selling and acquisition prices are related to the distance between distribution centers and customers. T...
متن کاملVenn Diagrams and Symmetric Chain Decompositions in the Boolean Lattice
We show that symmetric Venn diagrams for n sets exist for every prime n, settling an open question. Until this time, n = 11 was the largest prime for which the existence of such diagrams had been proven, a result of Peter Hamburger. We show that the problem can be reduced to finding a symmetric chain decomposition, satisfying a certain cover property, in a subposet of the Boolean lattice Bn, an...
متن کاملSet Families with a Forbidden Subposet
We asymptotically determine the size of the largest family F of subsets of {1, . . . , n} not containing a given poset P if the Hasse diagram of P is a tree. This is a qualitative generalization of several known results including Sperner’s theorem. Introduction We say that a poset P is a subposet of a poset P ′ if there is an injective map f : P → P ′ such that a 6P b implies f(a) 6P ′ f(b). A ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Electr. J. Comb.
دوره 22 شماره
صفحات -
تاریخ انتشار 2015