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4 papers · 2 filters
Congruences for Catalan and Motzkin numbers and related sequences
Emeric Deutsch, Bruce E. Sagan
We prove various congruences for Catalan and Motzkin numbers as well as related sequences. The common thread is that all these sequences can be expressed in terms of binomial coeff…
Proper partitions of a polygon and k-Catalan numbers
Bruce Sagan
Let P be a polygon whose vertices have been colored (labeled) cyclically with the numbers 1,2,...,c. Motivated by conjectures of Propp, we are led to consider partitions of P into…
GCD matrices, posets, and nonintersecting paths
Ercan Altinisik, Bruce E. Sagan, Naim Tuglu
We show that with any finite partially ordered set one can associate a matrix whose determinant factors nicely. As corollaries, we obtain a number of results in the literature abou…
Bounding quantities related to the packing density of 1(L+1)L...2
Martin Hildebrand, Bruce E. Sagan, Vincent Vatter
We bound several quantities related to the packing density of the patterns 1(L+1)L...2. These bounds sharpen results of Bóna, Sagan, and Vatter and give a new proof of the packing…