arXiv:1306.2930 Abstract | arXiv Analytics

arXiv:1306.2930 [math.CO]Abstract References Reviews Resources

Another proof of Wilmes' conjecture

Published 2013-06-12, updated 2015-08-01Version 4

We present a new proof of the monomial case of Wilmes' conjecture, which gives a formula for the coarsely-graded Betti numbers of the G-parking function ideal in terms of maximal parking functions of contractions of G. Our proof is via poset topology and relies on a theorem of Gasharov, Peeva, and Welker that connects the Betti numbers of a monomial ideal to the topology of its lcm-lattice.

Comments: 8 pages, 1 figure. v2: added reference to a recent preprint of Mohammadi and Shokrieh. v3: to appear in Discrete Math, v4: minor typo corrected

Categories: math.CO

Subjects: 05E40, 05C25, 13D02, 06B30

Keywords: conjecture, monomial case, monomial ideal, poset topology, coarsely-graded betti numbers

Related articles: Most relevant | Search more

arXiv:math/0009230 [math.CO] (Published 2000-09-26)

The conjecture cr(C_m\times C_n)=(m-2)n is true for all but finitely many n, for each m

Lev Glebsky, Gelasio Salazar

arXiv:math/0508537 [math.CO] (Published 2005-08-26)

On a conjecture of Widom

Alexei Borodin, Alexei Novikov

arXiv:math/0610977 [math.CO] (Published 2006-10-31)

New results related to a conjecture of Manickam and Singhi