Discrete morse functions from lexicographic orders

Transactions of the American Mathematical Society

Volumn 357, Issue 2, 2005, Pages 509-534

  Babson, Eric ^a   Hersh, Patricia ^a,b  

^a UNIVERSITY OF WASHINGTON   (United States)

^b MATHEMATICAL SCIENCES RESEARCH INSTITUTE   (United States)

Author keywords

Discrete Morse theory; Order complex; Partition; Poset

Indexed keywords

EID: 13844254237     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-04-03495-6     Document Type: Article

References (26)

1. E. Babson, A. Björner, S. Linusson, J. Shareshian and V. Welker, Complexes of not i-connected graphs, Topology 38 (1999), 271-299. MR1660341 (2000a:57001)
2. E. Babson and D. Kozlov, Group actions on posets, To appear in J. Algebra.
3. L. Billera and G. Hetyei, Linear inequalities for flags in graded partially ordered sets, J. Combin. Theory Ser. A 89 (2000), 77-104. MR1736134 (2001m:52011)
4. A. Bjorner, Shellable and Cohen-Macaulay partially ordered sets, Trans. Amer. Math. Soc. 260 (1980), no. 1, 159-183. MR0570784 (81i:06001)
5. A. Björner, Posets, regular CW complexes and Bruhat order, European J. Combin. 5 (1984), no. 1, 7-16. MR0746039 (86e:06002)
6. A. Björner, Topological Methods, in Handbook of Combinatorics (R. Graham, M. Grötschel and L. Lovasz, eds.), North-Holland, Amsterdam, 1993. MR1373690 (96m:52012)
7. A. Björner and M. Wachs, Bruhat order of Coxeter groups and shellability, Adv. in Math. 43 (1982), 87-100. MR0644668 (83i:20043)
8. A. Bjorner and M. Wachs, On lexicographically shellable posets, Trans. Amer. Math. Soc. 277 (1983), no. 1, 323-341. MR0690055 (84f:06004)
9. A. Björner and M. Wachs, Nonpure shellable complexes and posets I, Trans. Amer. Math. Soc. 348 (1996), 1299-1327. MR1333388 (96i:06008)
10. A. Björner and M. Wachs, Nonpure shellable complexes and posets II, Trans. Amer. Math. Soc. 349 (1997), 3945-3975. MR1401765 (98b:06008)
11. M. Chari, On discrete Morse functions and combinatorial decompositions, Discrete Math 217 (2000), no. 1-3, 101-113. MR1766262 (2001g:52016)
12. J. Folkman, The homology groups of a lattice, J. Math. Mech. 15 (1966), 631-636. MR0188116 (32:5557)
13. R. Forman, Morse theory for cell complexes, Adv. Math. 134 (1998), 90-145. MR1612391 (99b:57050)
14. P. Hersh, Lexicographic shellability for balanced complexes, J. Algebraic Combin. 17 (2003), no. 3, 225-254. MR2001670 (2004f:05190)
15. P. Hersh, On optimizing discrete Morse functions, Preprint 2003.
16. P. Hersh and R. Kleinberg, The refinement complex of the poset of partitions of a multiset, In preparation.
17. k[Λ](k, k), To appear in Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Integer Points in Polyhedra.
18. D. Kozlov, General lexicographic shellability and orbit arrangements, Ann. of Comb. 1 (1997), no. 1, 67-90. MR1474801 (98h:52023)
19. D. Kozlov, Complexes of directed trees, J. Combin. Theory Ser A 88 (1999), no. 1, 112-122. MR1713484 (2000j:05036)
20. G-C. Rota, On the foundations of combinatorial theory I: Theory of Möbius functions, Z. Wahrsch. 2 (1964), 340-368. MR0174487 (30:4688)
21. J. Shareshian, On the shellability of the order complex of the subgroup lattice of a finite group, Trans. Amer. Math. Soc. 353 (2001), no. 7, 2689-2703. MR1828468 (2002k:06006)
22. R. Stanley, Supersolvable lattices, Algebra Universalis 2 (1972), 197-217. MR0309815 (46:8920)
23. R. Stanley, Enumerative Combinatorics, vol. I. Wadsworth and Brooks/Cole, Pacific Grove, CA, 1986; second printing, Cambridge University Press, Cambridge/New York, 1997. MR0847717 (87j:05003)
24. R. Stanley, Combinatorics and Commutative Algebra, second ed., Birkhäuser, Boston, 1996. MR1453579 (98h:05001)
25. V. Welker, Direct sum decompositions of matroids and exponential structures, J. Combin. Theory Ser. B 63 (1995), no. 2, 222-244. MR1320168 (96e:05042)
26. G. Ziegler, On the poset of partitions of an integer, J. Combin. Theory Ser. A 42 (1986), no. 2, 215-222. MR0847552 (87k:06009)