000226836 001__ 226836
000226836 005__ 20181203024618.0
000226836 0247_ $$2doi$$a10.1016/j.jpaa.2016.09.001
000226836 022__ $$a0022-4049
000226836 02470 $$2ISI$$a000392783200002
000226836 037__ $$aARTICLE
000226836 245__ $$aCombinatorial presentation of multidimensional persistent homology
000226836 260__ $$aAmsterdam$$bElsevier$$c2017
000226836 269__ $$a2017
000226836 300__ $$a21
000226836 336__ $$aJournal Articles
000226836 520__ $$aA multifiltration is a functor indexed by Nr that maps any morphism to a monomorphism. The goal of this paper is to describe in an explicit and combinatorial way the natural Nr-graded R[x(1),...x(r)]-module structure on the homology of a multifiltration of simplicial complexes. To do that we study multifiltrations of sets and R-modules. We prove in particular that the Nr-graded R[x(1),...,x(r)]-modules that can occur as R-spans of multifiltrations of sets are the direct sums of monomial ideals. (C) 2016 Elsevier B.V. All rights reserved.
000226836 700__ $$aChacholski, W.$$uKTH, Dept Math, S-10044 Stockholm, Sweden
000226836 700__ $$aScolamiero, M.$$uEcole Polytech Fed Lausanne, Lab Topol & Neurosci, CH-1015 Lausanne, Switzerland
000226836 700__ $$aVaccarino, F.$$uPolitecn Torino, Dipartimento Sci Matemat, Cso Duca degli Abruzzi 24, I-10129 Turin, Italy
000226836 773__ $$j221$$k5$$q1055-1075$$tJournal Of Pure And Applied Algebra
000226836 909C0 $$0252139$$pUPHESS$$xU10968
000226836 909CO $$ooai:infoscience.tind.io:226836$$pSV$$particle
000226836 917Z8 $$x180122
000226836 937__ $$aEPFL-ARTICLE-226836
000226836 973__ $$aEPFL$$rREVIEWED$$sPUBLISHED
000226836 980__ $$aARTICLE