The cd-index of fans and posets

Kalle Karu

doi:10.1112/S0010437X06001928

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The number of flags in a complete fan, or more generally in an Eulerian poset, is encoded in the cd-index. We prove the non-negativity of the cd-index for complete fans, regular CW-spheres and Gorenstein* posets.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Ehrenborg, Richard and Karu, Kalle 2007. Decomposition theorem for the cd-index of Gorenstein* posets. Journal of Algebraic Combinatorics, Vol. 26, Issue. 2, p. 225.

Brenti, Francesco and Welker, Volkmar 2008. f-Vectors of barycentric subdivisions. Mathematische Zeitschrift, Vol. 259, Issue. 4, p. 849.

Frohmader, Andrew 2010. The Charney–Davis Conjecture for Certain Subdivisions of Spheres. Discrete & Computational Geometry, Vol. 43, Issue. 3, p. 705.

Бухштабер, Виктор Матвеевич Buchstaber, Victor Matveevich Ероховец, Николай Юрьевич and Erokhovets, Nikolai Yur'evich 2011. Многогранники, числа Фибоначчи, алгебры Хопфа и квазисимметрические функции. Успехи математических наук, Vol. 66, Issue. 2, p. 67.

Billera, Louis J. and Brenti, Francesco 2011. Quasisymmetric functions and Kazhdan-Lusztig polynomials. Israel Journal of Mathematics, Vol. 184, Issue. 1, p. 317.

Nevo, Eran Petersen, T. Kyle and Tenner, Bridget Eileen 2011. The γ-vector of a barycentric subdivision. Journal of Combinatorial Theory, Series A, Vol. 118, Issue. 4, p. 1364.

Nevo, Eran and Petersen, T. Kyle 2011. On γ-Vectors Satisfying the Kruskal–Katona Inequalities. Discrete & Computational Geometry, Vol. 45, Issue. 3, p. 503.

Murai, Satoshi and Nevo, Eran 2012. On the cd-index and γ-vector of S*-shellable CW-spheres. Mathematische Zeitschrift, Vol. 271, Issue. 3-4, p. 1309.

Blanco, Saúl A. 2013. Shortest path poset of Bruhat intervals. Journal of Algebraic Combinatorics, Vol. 38, Issue. 3, p. 585.

Karu, Kalle 2013. On the complete cd-index of a Bruhat interval. Journal of Algebraic Combinatorics, Vol. 38, Issue. 3, p. 527.

Ehrenborg, Richard and Readdy, Margaret 2014. Manifold arrangements. Journal of Combinatorial Theory, Series A, Vol. 125, Issue. , p. 214.

Murai, Satoshi and Yanagawa, Kohji 2014. Squarefree P-modules and the cd-index. Advances in Mathematics, Vol. 265, Issue. , p. 241.

Petersen, T. Kyle 2015. Eulerian Numbers. p. 203.

Ehrenborg, Richard Goresky, Mark and Readdy, Margaret 2015. Euler flag enumeration of Whitney stratified spaces. Advances in Mathematics, Vol. 268, Issue. , p. 85.

Fan, Neil J.Y. and He, Liao 2015. On the non-negativity of the complete cd-index. Discrete Mathematics, Vol. 338, Issue. 11, p. 2037.

Murai, Satoshi 2015. Combinatorial Methods in Topology and Algebra. Vol. 12, Issue. , p. 103.

Klee, Steven and Novik, Isabella 2016. LOWER BOUND THEOREMS AND A GENERALIZED LOWER BOUND CONJECTURE FOR BALANCED SIMPLICIAL COMPLEXES. Mathematika, Vol. 62, Issue. 2, p. 441.

Adamaszek, Michał and Hladký, Jan 2016. UPPER BOUND THEOREM FOR ODD‐DIMENSIONAL FLAG TRIANGULATIONS OF MANIFOLDS. Mathematika, Vol. 62, Issue. 3, p. 909.

Karu, Kalle 2016. M-vector analogue for the cd-index. Journal of Combinatorial Theory, Series A, Vol. 137, Issue. , p. 257.

Brenti, Francesco and Caselli, Fabrizio 2017. Peak algebras, paths in the Bruhat graph and Kazhdan–Lusztig polynomials. Advances in Mathematics, Vol. 304, Issue. , p. 539.

Download full list

Article contents

The cd-index of fans and posets

Abstract

Keywords

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

The cd-index of fans and posets

Abstract

Keywords

Save article to Kindle

Save article to Dropbox

Save article to Google Drive

Reply to: Submit a response

Your details

You have entered the maximum number of contributors

Conflicting interests