On P-partitions related to ordinal sums of posets
نویسندگان
چکیده
Using the inclusion–exclusion principle, we derive a formula of generating functions for P-partitions related to ordinal sums of posets. This formula simplifies computations for many variations of plane partitions, such as plane partition polygons and plane partitions with diagonals or double diagonals. We illustrate our method by several examples, some of which are new variations of plane partitions.
منابع مشابه
Partially Ordinal Sums and P-partitions
We present a method of computing the generating function fP (x) of P -partitions of a poset P . The idea is to introduce two kinds of transformations on posets and compute fP (x) by recursively applying these transformations. As an application, we consider the partially ordinal sum Pn of n copies of a given poset, which generalizes both the direct sum and the ordinal sum. We show that the seque...
متن کاملAggregation Functions Constructions, Characterizations, and Functional Equations
Ordinal sums have been introduced in many different contexts, e.g., for posets, semigroups, t-norms, copulas, aggregation operators, or quite recently for hoops. In this contribution, we focus on ordinal sums of t-norms acting on some bounded lattice which is not necessarily a chain or an ordinal sum of posets. Necessary and sufficient conditions are provided for an ordinal sum operation yieldi...
متن کاملOn the Number of Distributive Lattices
We investigate the numbers dk of all (isomorphism classes of) distributive lattices with k elements, or, equivalently, of (unlabeled) posets with k antichains. Closely related and useful for combinatorial identities and inequalities are the numbers vk of vertically indecomposable distributive lattices of size k. We present the explicit values of the numbers dk and vk for k < 50 and prove the fo...
متن کاملMatchings, cutsets, and chain partitions in graded posets
New properties that involve matchings, cutsets, or skipless chain partitions in graded posets are introduced and compared to familiar Sperner and chain partition properties. Related work is surveyed. We determine all possible combinations of these properties, with the exception of a long-standing open conjecture about L Y M posets, and provide a list of examples realizing these combinations.
متن کاملOrder dense injectivity of $S$-posets
In this paper, the notion of injectivity with respect to order dense embeddings in the category of $S$-posets, posets with a monotone action of a pomonoid $S$ on them, is studied. We give a criterion, like the Baer condition for injectivity of modules, or Skornjakov criterion for injectivity of $S$-sets, for the order dense injectivity. Also, we consider such injectivit...
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:
- Eur. J. Comb.
دوره 30 شماره
صفحات -
تاریخ انتشار 2009