منابع مشابه
k-Eulerian Posets
A poset P is called k-Eulerian if every interval of rank k is Eulerian. The class of k-Eulerian posets interpolates between graded posets and Eulerian posets. It is a straightforward observation that a 2k-Eulerian poset is also (2k+1)-Eulerian. We prove that the ab-index of a (2k+1)Eulerian poset can be expressed in terms of c = a + b, d = ab + ba and e2k+1 = (a − b)2k+1. The proof relies upon ...
متن کاملLevel Eulerian Posets
The notion of level posets is introduced. This class of infinite posets has the property that between every two adjacent ranks the same bipartite graph occurs. When the adjacency matrix is indecomposable, we determine the length of the longest interval one needs to check to verify Eulerianness. Furthermore, we show that every level Eulerian poset associated to an indecomposable matrix has even ...
متن کاملFlags and shellings of Eulerian cubical posets∗†
A cubical analogue of Stanley’s theorem expressing the cd-index of an Eulerian simplicial poset in terms of its h-vector is presented. This result implies that the cd-index conjecture for Gorenstein∗ cubical posets follows from Ron Adin’s conjecture on the non-negativity of his cubical h-vector for Cohen-Macaulay cubical posets. For cubical spheres the standard definition of shelling is shown t...
متن کاملFinite Eulerian posets which are binomial or Sheffer
In this paper we study finite Eulerian posets which are binomial or Sheffer. These important classes of posets are related to the theory of generating functions and to geometry. The results of this paper are organized as follows: (1) We completely determine the structure of Eulerian binomial posets and, as a conclusion, we are able to classify factorial functions of Eulerian binomial posets; (2...
متن کاملCharacterization of the factorial functions of Eulerian binomial and Sheffer posets
We completely characterize the factorial functions of Eulerian binomial posets. The factorial function B(n) either coincides with n!, the factorial function of the infinite Boolean algebra, or 2n−1, the factorial function of the infinite butterfly poset. We also classify the factorial functions for Eulerian Sheffer posets. An Eulerian Sheffer poset with binomial factorial function B(n) = n! has...
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ژورنال
عنوان ژورنال: Discussiones Mathematicae General Algebra and Applications
سال: 2023
ISSN: ['1509-9415', '2084-0373']
DOI: https://doi.org/10.7151/dmgaa.1407