共查询到20条相似文献,搜索用时 31 毫秒
1.
Hoda Bidkhori 《Journal of Combinatorial Theory, Series A》2012,119(3):765-787
In this paper we study finite Eulerian posets which are binomial, Sheffer or triangular. 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:
- •
- We completely determine the structure of Eulerian binomial posets and, as a conclusion, we are able to classify factorial functions of Eulerian binomial posets.
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- We give an almost complete classification of factorial functions of Eulerian Sheffer posets by dividing the original question into several cases.
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- In most cases above, we completely determine the structure of Eulerian Sheffer posets, a result stronger than just classifying factorial functions of these Eulerian Sheffer posets.
2.
Michelle L. Wachs 《Journal of Algebraic Combinatorics》1999,9(2):173-207
We generalize results of Calderbank, Hanlon and Robinson on the representation of the symmetric group on the homology of posets of partitions with restricted block size. Calderbank, Hanlon and Robinson consider the cases of block sizes that are congruent to 0 mod d and 1 mod d for fixed d. We derive a general formula for the representation of the symmetric group on the homology of posets of partitions whose block sizes are congruent to k mod d for any k and d. This formula reduces to the Calderbank-Hanlon-Robinson formulas when k = 0, 1 and to formulas of Sundaram for the virtual representation on the alternating sum of homology. Our results apply to restricted block size partition posets even more general than the k mod d partition posets. These posets include the lattice of partitions whose block sizes are bounded from below by some fixed k. Our main tools involve the new theory of nonpure shellability developed by Björner and Wachs and a generalization of a technique of Sundaram which uses Whitney homology to compute homology representations of Cohen-Macaulay posets. An application to subspace arrangements is also discussed. 相似文献
3.
Thomas Lam 《Journal of Combinatorial Theory, Series A》2008,115(3):466-484
We study signed differential posets, a signed version of differential posets. These posets satisfy enumerative identities which are signed analogues of those satisfied by differential posets. Our main motivations are the sign-imbalance identities for partition shapes originally conjectured by Stanley, now proven in [T. Lam, Growth diagrams, domino insertion and sign-imbalance, J. Combin. Theory Ser. A 107 (2004) 87-115; A. Reifergerste, Permutation sign under the Robinson-Schensted-Knuth correspondence, Ann. Comb. 8 (2004) 103-112; J. Sjöstrand, On the sign-imbalance of partition shapes, J. Combin. Theory Ser. A 111 (2005) 190-203]. We show that these identities result from a signed differential poset structure on Young's lattice, and explain similar identities for Fibonacci shapes. 相似文献
4.
In this paper, posets which may not be dcpos are considered. In terms of the Scott topology on posets, the new concept of
quasicontinuous posets is introduced. Some properties and characterizations of quasicontinuous posets are examined. The main
results are: (1) a poset is quasicontinuous iff the lattice of all Scott open sets is a hypercontinuous lattice; (2) the directed
completions of quasicontinuous posets are quasicontinuous domains; (3) A poset is continuous iff it is quasicontinuous and
meet continuous, generalizing the relevant result for dcpos.
Supported by the NSF of China (10371106, 10410638) and by the Fund (S0667-082) from Nanjing University of Aeronautics and
Astronautics. 相似文献
5.
《Discrete Mathematics》2022,345(1):112629
Upper homogeneous finite type (upho) posets are a large class of partially ordered sets with the property that the principal order filter at every vertex is isomorphic to the whole poset. Well-known examples include k-ary trees, the grid graphs, and the Stern poset. Very little is known about upho posets in general. In this paper, we construct upho posets with Schur-positive Ehrenborg quasisymmetric functions, whose rank-generating functions have rational poles and zeros. We also categorize the rank-generating functions of all planar upho posets. Finally, we prove the existence of an upho poset with an uncomputable rank-generating function. 相似文献
6.
《Discrete Mathematics》2023,346(2):113218
We prove a conjecture of Morier-Genoud and Ovsienko that says that rank polynomials of the distributive lattices of lower ideals of fence posets are unimodal. We do this by proving a stronger version of the conjecture due to McConville, Sagan, and Smyth. Our proof involves introducing a related class of posets, which we call circular fence posets and showing that their rank polynomials are symmetric. We also apply the recent work of Elizalde, Plante, Roby, and Sagan on rowmotion on fences and show many of their homomesy results hold for the circular case as well. 相似文献
7.
Siaw-Lynn Ng 《Order》2004,21(1):1-5
We present a characterisation of posets of size n with linear discrepancy n − 2. These are the posets that are “furthest” from a linear order without being an antichain.
This revised version was published online in September 2006 with corrections to the Cover Date. 相似文献
8.
In this paper, some properties of order topology and bi-Scott topology on a poset are obtained. Order-convergence in posets
is further studied. Especially, a sufficient and necessary condition for order-convergence to be topological is given for
some kind of posets. 相似文献
9.
We consider the amalgamation of bounded involution posets over a strictly directed graph as applied to orthomodular lattices,
orthomodular posets or orthoalgebras. In the finite setting, we show that the order dimension of the amalgamation does not
exceed that of the amalgamated structures by more than one. We also present conditions under which equality obtains.
相似文献
10.
Jānis Cīrulis 《Central European Journal of Mathematics》2008,6(1):189-190
We characterise those Hilbert algebras that are relatively pseudocomplemented posets.
相似文献
11.
本文引入了代数的局部完备集,FS-局部dcpo,局部稳定映射等概念.主要结果是:以局部Scott连续映射为态射的代数的局部完备集范畴,以局部稳定映射为态射的代数的局部完备集范畴以及以局部Scott连续映射为态射的FS-局部dcpo范畴都是笛卡儿闭范畴. 相似文献
12.
We study which infinite posets have simple cofinal subsets such as chains, or decompose canonically into such subsets. The posets of countable cofinality admitting such a decomposition are characterized by a forbidden substructure; the corresponding problem for uncountable cofinality remains open. 相似文献
13.
A new concept Graded Finite Poset is proposed in this paper.Through discussing some basic properties of it,we come to that the direct product of graded finite posets is connected if and only if every graded finite poset is connected.The graded function of a graded finite poset is unique if and only if the graded finite poset is connected. 相似文献
14.
Richard Ehrenborg 《Journal of Combinatorial Theory, Series A》2007,114(2):339-359
We give a complete classification of 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 Sheffer factorial function D(n) identical to that of the infinite Boolean algebra, the infinite Boolean algebra with two new coatoms inserted, or the infinite cubical poset. Moreover, we are able to classify the Sheffer factorial functions of Eulerian Sheffer posets with binomial factorial function B(n)=2n−1 as the doubling of an upside-down tree with ranks 1 and 2 modified. When we impose the further condition that a given Eulerian binomial or Eulerian Sheffer poset is a lattice, this forces the poset to be the infinite Boolean algebra BX or the infinite cubical lattice . We also include several poset constructions that have the same factorial functions as the infinite cubical poset, demonstrating that classifying Eulerian Sheffer posets is a difficult problem. 相似文献
15.
In this article we describe a very efficient method to construct pairwise non-isomorphic posets (equivalently, T
0 topologies). We also give the results obtained by a computer program based on this algorithm, in particular the numbers of non-isomorphic posets on 15 and 16 points and the numbers of labelled posets and topologies on 17 and 18 points. 相似文献
16.
In this paper,the concepts of the essential topology and the density topology of dcpos are generalized to the setting of general posets.Basic properties of the essential topology and relations with other intrinsic topologies are explored.Comparisons between the density topology and the measurement topology are made.Via the essential topology,the density topology and the measurement topology,we obtain properties and characterizations of bases of continuous posets.We also provide some new conditions for a continuous poset to be an algebraic poset. 相似文献
17.
Robert A. Proctor 《Journal of Algebraic Combinatorics》1999,9(1):61-94
d-Complete posets are defined to be posets which satisfy certain local structural conditions. These posets play or conjecturally play several roles in algebraic combinatorics related to the notions of shapes, shifted shapes, plane partitions, and hook length posets. They also play several roles in Lie theory and algebraic geometry related to -minuscule elements and Bruhat distributive lattices for simply laced general Weyl or Coxeter groups, and to -minuscule Schubert varieties. This paper presents a classification of d-complete posets which is indexed by Dynkin diagrams. 相似文献
18.
Jim Lawrence 《Discrete Mathematics》2021,344(8):112437
Parity representations, introduced in this paper, comprise a new method of representation of posets that yields insight into the combinatorics of the poset of all intervals of a poset. Results here generalize some results previously obtained for the face lattices of binary partition polytopes. 相似文献
19.
20.
Michał Kukieła 《Order》2009,26(2):119-124
Call a poset reversible if every of its order-preserving self-bijections is an automorphism. Call two posets bijectively related
if from each of the two posets exists an order-preserving bijection to the other. We present two examples of pairs of non-isomorphic,
bijectively related posets and an example of a non-reversible poset that is bijectively related only to itself. Also, three
classes of reversible posets are described and a sufficient condition for an order-preserving bijection to be an isomorphism
is presented. 相似文献