Counting words without strictly increasing subwords of fixed length

2025/11/17 by Sekhon, Senan
#Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2511.13287

Abstract

In this paper, we derive exact formulas for generating functions counting the number of n-ary words avoiding strictly increasing subwords of length k, and provide some applications of these formulas.

Citations

• Penney's game for permutations
• Smirnov words and the Delta Conjectures
• Words restricted by 3-letter generalized multipermutation patterns
• The Goulden-Jackson Cluster Method: Extensions, Applications and Implementations

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