Báo cáo toán học: "Traces Without Maximal Chains" pptx

... x ∗ , is a minimal (respectively, maximal) solution of (1) in Title Suppressed Due to Excessive Length 21 References 1. Figueroa, R, Pouso, RL: Minimal and maximal solutions to second-order b ... minimal solution in Y , but the converse is false in general, and an analgous remark is true for maximal and greatest solutions. Interestingly, we will show that problem (1) may have minimal (ma...

Ngày tải lên: 20/06/2014, 20:20

... expression takes a simpler form: the electronic journal of combinatorics 14 (2007), #R11 8 Permutations without long decreasing subsequences and random matrices Piotr ´ Sniady Institute of Mathematics University

Ngày tải lên: 07/08/2014, 15:22

... excluded fa mily is 2 [k] . In [10] it is proved (among others) t hat if we change 2 [k] to the maximal chain C k = {∅, [1], [2], , [k]} in Theorem 1.1, then the only extremal families are {F ... ≤  n−1 k−1  −  n−k−1 k−1  + 1. 2 Proof of Theorem 1.3 First we prove a lemma stating that if we want to have an “almost” maximal chain C − k = {[1], [2], , [k]} as trace, then much smaller fa...

Ngày tải lên: 07/08/2014, 21:21

... the possible orbits and providing 2-distinguishing colorings for graphs with 6-orbits, and graphs without 6-orbits, but with 3-orbits. Clearly graphs with largest orbit size 2 can be 2-distinguished.

Ngày tải lên: 07/08/2014, 06:20

... This completes (14) and hence the Claim. Remark. The above claim can also be stated and proven without the use of infinitesimals, giving a bound on E[X s+∆s − X s ]. In that case there would be ... centered on lowering the size of | S | in terms of D . Our main result has also been shown (indeed, without the logarithmic term for k ≥ 3) in our joint paper [1] by quite different techniques. 1...

Ngày tải lên: 07/08/2014, 06:22

... cardinality of to be finite, = {a 1 , ,a N }, before letting it tend to infinity. Let π ω be the maximal isobaric divided difference, that is, the operator such that the image of a λ := a λ 1 1 ···a λ N N is

Ngày tải lên: 07/08/2014, 06:22

... the obtained  H n is presented by Eq. 5. Now we want to determine the minimal appropriate i (providing us the maximal appropriate a n−i ), which will give us the highest lower bound for d(  H n ). Instead ... (2002), #R23 8 The proof is simple: Consider the source node s and any other node v of  H n+1 . Without loss of generality, suppose that s ∈  H 0 n ,where  H 0 n is one of the t...

Ngày tải lên: 07/08/2014, 06:23

... permutation (or a poset) π to be layeredontop(or LOT ) if each of its maximal elements is greater than any non -maximal element. The set of these maximal elements is called the final layer of π (even if π ... ∈ S n }, in other words, that there is a permutation in S n among the maximal Π-containing words in [n] n . Consider any maximal Π-containing word σ ∈ [n] n .Letn i be the multip...

Ngày tải lên: 07/08/2014, 07:21

... itself is the desired sunflower. Otherwise Z :=  X∈T X is a set of size at most (t − 1)k, which, by maximality, meets every member of F . By the pigeonhole principal, some element z ∈ Z must lie in ... indicating the maximum over L ∈Cof the maximum size of a k-uniform family F of elements member of L without a sunflower S of size t contained in F . The point of such a function is to identify...

Ngày tải lên: 07/08/2014, 13:21

Ngày tải lên: 07/08/2014, 13:21