Inversion sequences avoiding 021 and another pattern of length four
DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE(2023)
摘要
We study the enumeration of inversion sequences that avoid pattern 021 and another pattern of length four. We determine the generating trees for all possible pattern pairs and compute the corresponding generating functions. We introduce the concept of d-regular generating trees and conjecture that for any 021-avoiding pattern tau, the generating tree T({021, tau}) is d-regular for some integer d.
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关键词
Pattern-avoiding inversion sequences,generating functions,generating trees,kernel method,Catalan numbers,Motzkin numbers
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