Symmetric Chain Decomposition of Necklace Posets
نویسنده
چکیده
A finite ranked poset is called a symmetric chain order if it can be written as a disjoint union of rank-symmetric, saturated chains. If P is any symmetric chain order, we prove that P/Zn is also a symmetric chain order, where Zn acts on Pn by cyclic permutation of the factors.
منابع مشابه
A Decomposition of Parking Functions by Undesired Spaces
There is a well-known bijection between parking functions of a fixed length and maximal chains of the noncrossing partition lattice which we can use to associate to each set of parking functions a poset whose Hasse diagram is the union of the corresponding maximal chains. We introduce a decomposition of parking functions based on the largest number omitted and prove several theorems about the c...
متن کاملThe symmetric monoidal closed category of cpo $M$-sets
In this paper, we show that the category of directed complete posets with bottom elements (cpos) endowed with an action of a monoid $M$ on them forms a monoidal category. It is also proved that this category is symmetric closed.
متن کاملThe necklace poset is a symmetric chain order
Let Nn denote the quotient poset of the Boolean lattice, Bn, under the relation equivalence under rotation. Griggs, Killian, and Savage proved that Np is a symmetric chain order for prime p. In this paper, we settle the question of whether this poset is a symmetric chain order for all n by providing an algorithm that produces a symmetric chain decompostion (or SCD). We accomplish this by modify...
متن کاملDECOMPOSITION METHOD FOR SOLVING FULLY FUZZY LINEAR SYSTEMS
In this paper, we investigate the existence of a positive solution of fully fuzzy linear equation systems. This paper mainly to discuss a new decomposition of a nonsingular fuzzy matrix, the symmetric times triangular (ST) decomposition. By this decomposition, every nonsingular fuzzy matrix can be represented as a product of a fuzzy symmetric matrix S and a fuzzy triangular matrix T.
متن کاملSome Sufficient Conditions for Finding a Nesting of the Normalized Matching Posets of Rank 3
Given a graded poset P , consider a chain decomposition C of P . If |C1| ≤ |C2| implies that the set of the ranks of elements in C1 is a subset of the ranks of elements in C2 for any chains C1, C2 ∈ C, then we say C is a nested chain decomposition (or nesting, for short) of P , and P is said to be nested. In 1970s, Griggs conjectured that every normalized matching rank-unimodal poset is nested....
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 19 شماره
صفحات -
تاریخ انتشار 2012