Proofs of two conjectures of Kenyon and Wilson on Dyck tilings

Details Proofs of two conjectures of Kenyon and Wilson on Dyck tilings Proofs of two conjectures of Kenyon and Wilson on Dyck tilings

2011-08-29

arxiv.org/abs/1108.5558v1

Mathematics

Combinatorics

21 pages, 19 figures

Scientific paper

Recently, Kenyon and Wilson introduced a certain matrix $M$ in order to compute pairing probabilities of what they call the double-dimer model. They showed that the absolute value of each entry of the inverse matrix $M^{-1}$ is equal to the number of certain Dyck tilings of a skew shape. They conjectured two formulas on the sum of the absolute values of the entries in a row or a column of $M^{-1}$. In this paper we prove the two conjectures. As a consequence we obtain that the sum of the absolute values of all entries of $M^{-1}$ is equal to the number of complete matchings. We also find a bijection between Dyck tilings and complete matchings.

Affiliated with

Also associated with

No associations

Rating

Proofs of two conjectures of Kenyon and Wilson on Dyck tilings does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Proofs of two conjectures of Kenyon and Wilson on Dyck tilings, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Proofs of two conjectures of Kenyon and Wilson on Dyck tilings will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-126396