Tight combinatorial manifolds and graded Betti numbers

Shinji Murai1
1Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Toyonaka, Japan

Tóm tắt

Từ khóa


Tài liệu tham khảo

Avramov, L.L., Conca, A., Iyengar, S.B.: Subadditivity of syzygies of Koszul algebras. Math. Ann. 361, 511–534 (2015)

Bagchi, B.: The mu vector, Morse inequalities and a generalized lower bound theorem for locally tame combinatorial manifolds. arXiv:1405.5675

Bagchi, B.: A tightness criterion for homology manifolds with or without boundary. Eur. J. Comb. 46, 10–15 (2015)

Bagchi, B., Datta, B.: On stellated spheres and a tightness criterion for combinatorial manifolds. Eur. J. Comb. 36, 294–313 (2014)

Barnette, D.W.: The minimum number of vertices of a simple polytope. Israel J. Math. 10, 121–125 (1971)

Barnette, D.W.: A proof of the lower bound conjecture for convex polytopes. Pacific J. Math. 46, 349–354 (1973)

Bigatti, A.: Upper bounds for the Betti numbers of a given Hilbert function. Commun. Algebra 21, 2317–2334 (1993)

Brehm, U., Kühnel, W.: Combinatorial manifolds with few vertices. Topology 26, 465–473 (1987)

Bruns, W., Herzog, J.: Cohen-Macaulay rings, Revised edn. Cambridge University Press, Cambridge (1993)

Burton, B.A., Datta, B., Singh, N., Spreer, J.: Separation index of graphs and stacked 2-spheres. arXiv:1403.5862

Datta, B., Murai, S.: On stacked triangulated manifolds. arXiv:1407.6767

Datta, B., Singh, N.: An infinite family of tight triangulations of manifolds. J. Comb. Theory Ser. A 120, 2148–2163 (2013)

Effenberger, F.: Stacked polytopes and tight triangulations of manifolds. J. Comb. Theory Ser. A 118, 1843–1862 (2011)

Eliahou, S., Kervaire, M.: Minimal resolutions of some monomial ideals. J. Algebra 129, 1–25 (1990)

Fernández-Ramos, O., Gimenez, P.: Regularity $$3$$ 3 in edge ideals associated to bipartite graphs. J. Algebraic Comb. 39, 919–937 (2014)

Flores, A.: Über $$n$$ n -dimensionale Komplexe, die im $$R_{2n+1}$$ R 2 n + 1 absolut selbstverschlungen sind. Ergeb. Math. Kolloq. 6, 4–7 (1933/34)

Fogelsanger, A.: The generic rigidity of minimal cycles. Ph.D. Thesis, Cornell University (1988)

Herzog, J., Hibi, T.: Monomial ideals. Graduate Texts in Mathematics. Springer, London (2011)

Herzog, J., Srinivasan, H.: A note on the subadditivity problem for maximal shifts in free resolutions. MSRI Proc. (to appear). arXiv:1303.6214

Hulett, H.A.: Maximum Betti numbers of homogeneous ideals with a given Hilbert function. Commun. Algebra 21, 2335–2350 (1993)

Kalai, G.: Rigidity and the lower bound theorem. I. Invent. Math. 88, 125–151 (1987)

Kühnel, W.: Tight polyhedral submanifolds and tight triangulations. Lecture Notes in Math, vol. 1612. Springer, Berlin (1995)

Kühnel, W., Lutz, F.H.: A census of tight triangulations. In: Discrete Geometry and Rigidity, Budapest, 1999, Period. Math. Hungar, vol. 39, pp. 161–183 (1999)

Lutz, F.H.: Triangulated manifolds with few vertices: combinatorial manifolds. arXiv:math.0506372

Lutz, F.H., Sulanke, T., Swartz, E.: $$f$$ f -vectors of $$3$$ 3 -manifolds. Electron. J. Comb. 16, 33 (2009) (Research paper R13)

Macaulay, F.S.: Some properties of enumeration in the theory of modular systems. Proc. Lond. Math. Soc. 26, 531–555 (1927)

Migliore, J., Nagel, U.: Reduced arithmetically Gorenstein* schemes and simplicial polytopes with maximal Betti numbers. Adv. Math. 180, 1–63 (2003)

Murai, S., Nevo, E.: On the generalized lower bound conjecture for polytopes and spheres. Acta Math. 210, 185–202 (2013)

Murai, S., Nevo, E.: On $$r$$ r -stacked triangulated manifolds. J. Algebraic Comb. 39, 373–388 (2014)

Novik, I., Swartz, E.: Socles of Buchsbaum modules, complexes and posets. Adv. Math. 222, 2059–2084 (2009)

Novik, I., Swartz, E.: Applications of Klee’s Dehn-Sommerville relations. Discrete Comput. Geom. 42, 261–276 (2009)

Novik, I., Swartz, E.: Face numbers of pseudomanifolds with isolated singularities. Math. Scand. 110, 198–222 (2012)

Pardue, K.: Deformation classes of graded modules and maximal Betti numbers. Ill. J. Math. 40, 564–585 (1996)

Spanier, E.H.: Algebraic topology. Springer, New York (1981)

Spreer, J.: A necessary condition for the tightness of odd-dimensional combinatorial manifolds. arXiv:1405.5962

Stanley, R.P.: Combinatorics and commutative algebra, 2nd edn. Birkhäuser, Boston (1996)

Swartz, E.: Thirty-five years and counting. arXiv:1411.0987

Tay, T.-S.: Lower-bound theorems for pseudomanifolds. Discrete Comput. Geom. 13, 203–216 (1995)

Terai, N., Hibi, T.: Computation of Betti numbers of monomial ideals associated with stacked polytopes. Manuscripta Math. 92, 447–453 (1997)

van Kampen, E.R.: Komplexe in euklidischen Räumen. Abh. Math. Sem. Univ. Humburg 9(72–78), 152–153 (1933)

Ziegler, G.M.: Lectures on polytopes. Graduate Texts in Mathematics, vol. 152. Springer (2007)