63 citations · 131 across the 29 of their papers we have counts for
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Multi-colored dimer models in one-dimension: lattice paths and generalized Rogers--Ramanujan identities
Keiichi Shigechi
We define and study multi-colored dimer models on a segment and on a circle. The multivariate generating functions for the dimer models satisfy the recurrence relations similar to…
Rational Dyck tilings
Keiichi Shigechi
We introduce rational Dyck tilings, or -Dyck tilings, and study them by the decomposition into -Dyck tilings. This decomposition allows us to make use of combinatoria…
Generalized Dellac configurations
Keiichi Shigechi
We study combinatorics of two generalizations of Dellac configurations. First, we establish a correspondence between a generalized Dellac configuration with three parameters and a…
Rational Dyck paths and decompositions
Keiichi Shigechi
We study combinatorial properties of a rational Dyck path by decomposing it into a tuple of Dyck paths. The combinatorial models such as -Stirling permutations, -ary tree…
Dyck tilings of type
Keiichi Shigechi
We introduce and study cover-inclusive and cover-exclusive Dyck tilings of type . It is shown that the generating functions of Dyck tilings of type are expressed in terms of…