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f-vectors and h-vectors of simplicial posets

Richard P. Stanley
1991 Journal of Pure and Applied Algebra  
A simplicial poset is a (finite) poset P with d such that every interval [6, x] is a boolean algebra. Simplicial posets are generalizations of simplicial complexes.  ...  ., f-vectors and h-vectors of simplicial posets, Journal of Pure and Applied Algebra 71 (1991) 319-331.  ...  Introduction A sirnpliciul post [16, p. 1351 (also called a boolean complex [9, p. 1301 and a poset of boolean type [3, 42.31 ) isaposetPwith6(i.e.  ... 
doi:10.1016/0022-4049(91)90155-u fatcat:umultoc3wre75bwwsidxleoxle

Boolean functions on high-dimensional expanders [article]

Yotam Dikstein, Irit Dinur, Yuval Filmus, Prahladh Harsha
2019 arXiv   pre-print
Using this definition, we describe an analogue of the Fourier expansion and the Fourier levels of the Boolean hypercube for simplicial complexes.  ...  We initiate the study of Boolean function analysis on high-dimensional expanders.  ...  The goal of this work is to connect these two threads of research, by introducing Boolean function analysis on high-dimensional expanders. We study Boolean functions on simplicial complexes.  ... 
arXiv:1804.08155v3 fatcat:z73c2zsexzbjnn27qyunuvblcy

Iterated homology and decompositions of simplicial complexes

Art M. Duval, Ping Zhang
2001 Israel Journal of Mathematics  
Kalai has conjectured that a simplicial complex can be partitioned into Boolean algebras at least as roughly as a shifting-preserving collapse sequence of its algebraically shifted complex.  ...  This would imply a long-standing conjecture made (separately) by Garsia and Stanley concerning partitions of Cohen-Macaulay complexes into Boolean intervals.  ...  A shifting-preserving collapse sequence (see Definition 4.3) is a sequence of deletions of Boolean intervals from a simplicial complex, leaving a shifted simplicial complex at each step.  ... 
doi:10.1007/bf02802509 fatcat:jw45fvy3fnabzpkdyjupq7n5mm

Complexes of injective words and their commutation classes

Jakob Jonsson, Volkmar Welker
2009 Pacific Journal of Mathematics  
We study Boolean cell complexes of injective words over S and their commutation classes. This generalizes work by Farmer and by Björner and Wachs on the complex of all injective words.  ...  Specifically, for an abstract simplicial complex ∆, we consider the Boolean cell complex Γ(∆) whose cells are indexed by all injective words over the sets forming the faces of ∆.  ...  All our simplicial complexes and Boolean cell complexes are assumed to be finite.  ... 
doi:10.2140/pjm.2009.243.313 fatcat:dimztqapdzcfbbfagbbi4qxsya

Complexes of Injective Words and Their Commutation Classes [article]

Jakob Jonsson, Volkmar Welker
2007 arXiv   pre-print
We study Boolean cell complexes of injective words over S and their commutation classes. This generalizes work by Farmer and by Björner and Wachs on the complex of all injective words.  ...  All our simplicial complexes and Boolean cell complexes are assumed to be finite.  ...  Recall that a Boolean cell complex is a regular CW-complex for which the poset of faces of each cell is a Boolean lattice. Clearly, simplicial complexes are special cases of Boolean cell complexes.  ... 
arXiv:0712.2143v1 fatcat:gpwn4l4oorgfnf244mm3sh5jmu

A Macaulay2 Package for Stanley Simplicial Poset Ideals [article]

Nathan Nichols
2021 arXiv   pre-print
This package provides functions for working with simplicial posets and calculating their generalized Stanley-Reisner ideals.  ...  For practical purposes, we also introduce of a new random model for a class of simplicial posets which generalizes existing models for random simplicial complexes such as the Kahle model.  ...  The idea behind the model implemented by the function randSimplicialPoset is to define a deterministic function Θ(∆ 1 , ∆ 2 ) that takes two abstract simplicial complexes ∆ 1 and ∆ 2 on the same set of  ... 
arXiv:2009.10859v2 fatcat:lpgmvlqwmbhglmrhyzgrttdrsi

Consistency Results in Topology and Homotopy Theory

Jaykov Foukzon
2015 Pure and Applied Mathematics Journal  
≤N 1 and size N 2 in .  ...  Main results is: (1) let κ be an inaccessible cardinal and H k is a set of all sets having hereditary size less then κ, then Con(ZFC + (V = H k )), (2) there is a Lindelöf T 3 indestructible space of pseudocharacter  ...  We assume that any spaces will be simplicial sets, and maps and function complexes will be unbased.  ... 
doi:10.11648/j.pamj.s.2015040101.11 fatcat:fa7berac2narzf4jx5pzlnvehe

Page 420 of Mathematical Reviews Vol. , Issue 2003A [page]

2003 Mathematical Reviews  
Summary: “Kalai has conjectured that a simplicial complex can be partitioned into Boolean algebras at least as roughly as a shifting- preserving collapse sequence of its algebraically shifted complex.  ...  In particular, then, a simplicial complex could (conjecturally) be partitioned into Boolean intervals whose sizes are indexed by its iterated Betti numbers, a generalization of ordinary homology Betti  ... 

Random Uniform and Pure Random Simplicial Complexes [article]

Klas Markström, Trevor Pinto
2020 arXiv   pre-print
Finally we use the equivalence between simplicial complexes and monotone boolean functions to study the behaviour of typical such functions.  ...  We also study the random pure simplicial complex of dimension d, generated by letting any subset of size d+1 of a set of n vertices be a facet with probability p and considering the simplicial complex  ...  However, monotone Boolean functions and simplicial func-tions are equivalent object and we here present his result in terms of simplicial complexes.  ... 
arXiv:2001.01933v1 fatcat:bvkcpqirpzcr7mquon3lolgqty

Homotopy Type of the Boolean Complex of a Coxeter System [article]

Kari Ragnarsson, Bridget Eileen Tenner
2009 arXiv   pre-print
This simplicial poset defines a cell complex, called the boolean complex.  ...  One implication of these results is that the boolean complex is contractible if and only if a generator of the Coxeter system is in the center of the group. of these results is that the boolean complex  ...  The authors are grateful to Patricia Hersh and Richard Ehrenborg for helpful discussions at the onset of this work, as well as to John Shareshian for thoughtful feedback and suggestions, and the comments  ... 
arXiv:0806.0906v3 fatcat:rhpsyrxqrfe7reflrkbh3hyybq

On the topology of a boolean representable simplicial complex [article]

Stuart Margolis, John Rhodes, Pedro V. Silva
2015 arXiv   pre-print
In the case of dimension 2, it is shown that boolean representable simplicial complexes have the homotopy type of a wedge of spheres of dimensions 1 and 2.  ...  It is proved that fundamental groups of boolean representable simplicial complexes are free and the rank is determined by the number and nature of the connected components of their graph of flats for dimension  ...  The third author was partially supported by CNPq (Brazil) through a BJT-A grant (process 313768/2013-7) and CMUP (UID/MAT/00144/2013), which is funded by FCT (Portugal) with national (MEC) and European  ... 
arXiv:1510.05113v1 fatcat:6nga2h5y7rdmxo6tqnppfwdfrq

Homotopy type of the boolean complex of a Coxeter system

Kári Ragnarsson, Bridget Eileen Tenner
2009 Advances in Mathematics  
This simplicial poset defines a cell complex, called the boolean complex.  ...  One implication of these results is that the boolean complex is contractible if and only if a generator of the Coxeter system is in the center of the group.  ...  , and the comments of a dedicated referee.  ... 
doi:10.1016/j.aim.2009.05.007 fatcat:34zw4txb3rdibdaqframyp6ux4

On the topology of a boolean representable simplicial complex

Stuart Margolis, John Rhodes, Pedro V. Silva
2017 International journal of algebra and computation  
In the case of dimension 2, it is shown that boolean representable simplicial complexes have the homotopy type of a wedge of spheres of dimensions 1 and 2.  ...  It is proved that fundamental groups of boolean representable simplicial complexes are free and the rank is determined by the number and nature of the connected components of their graph of flats for dimension  ...  The third author was partially supported by CNPq (Brazil) through a BJT-A grant (process 313768/2013-7) and CMUP (UID/MAT/00144/2013), which is funded by FCT (Portugal) with national (MEC) and European  ... 
doi:10.1142/s0218196717500072 fatcat:mwtxv7gtnza6lj5xyk5cm6zn6u

Simplicial rtd-based cellular nonlinear networks

P. Julian, R. Dogaru, M. Itoh, M. Hanggi, L.O. Chua
2003 IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications  
Recently, a novel structure called the simplicial cellular neural network (CNN) has been introduced [1], which permits to implement any Boolean/Gray-level function of any number of variables.  ...  This paper is devoted to explore novel circuit architectures for the implementation of the simplicial CNN based on resonant tunneling diodes.  ...  This structure has been shown to produce Boolean functions with a complexity of , although it has not been shown yet that it is able to produce all Boolean functions of nine inputs (of special interest  ... 
doi:10.1109/tcsi.2003.809819 fatcat:2juu2262xjc7tn72pj7cvf4i3e

f-Vectors of Barycentric Subdivisions [article]

Francesco Brenti, Volkmar Welker
2006 arXiv   pre-print
For a simplicial complex or more generally Boolean cell complex Δ we study the behavior of the f- and h-vector under barycentric subdivision.  ...  For a general (d-1)-dimensional simplicial complex Δ the h-polynomial of its n-th iterated subdivision shows convergent behavior.  ...  The prime example of a Boolean cell complex is a simplicial complex.  ... 
arXiv:math/0606356v1 fatcat:ut4fbedvfveyhiolpf6pkuzdqu
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