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PreprintCC BY 4.0HAL

COUNTING 3-LETTER SUBWORDS IN AN ASCENT SEQUENCE

  • Toufik Mansour
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Abstract

Ascent sequences have become an important object of study in enumerative combinatorics due to their rich structure and connections with several combinatorial classes. In this paper, we develop a general method to analyze the generating function that counts the total number of occurrences of a fixed 3-letter subword pattern τ in ascent sequences of length n, refined by the number of ascents. Our method provides a unified framework for studying subword pattern occurrences in these sequences. As applications of the method, we investigate in detail the cases τ = 000, 001, 011, 012, 100, 110, and 210, deriving the corresponding generating functions and highlighting structural differences between these patterns.

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Cite

BibTeXRIS
BibTeX
@misc{mansour2026counting,
  title = {{COUNTING 3-LETTER SUBWORDS IN AN ASCENT SEQUENCE}},
  author = {Toufik Mansour},
  howpublished = {HAL},
  year = {2026},
  month = oct,
  url = {https://hal.science/hal-05833872v1},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - COUNTING 3-LETTER SUBWORDS IN AN ASCENT SEQUENCE
AU  - Toufik Mansour
PY  - 2026
DA  - 2026/10/22
PB  - HAL
UR  - https://hal.science/hal-05833872v1
AB  - Ascent sequences have become an important object of study in enumerative combinatorics due to their rich structure and connections with several combinatorial classes. In this paper, we develop a general method to analyze the generating function that counts the total number of occurrences of a fixed 3-letter subword pattern τ in ascent sequences of length n, refined by the number of ascents. Our method provides a unified framework for studying subword pattern occurrences in these sequences. As applications of the method, we investigate in detail the cases τ = 000, 001, 011, 012, 100, 110, and 210, deriving the corresponding generating functions and highlighting structural differences between these patterns.
ER  -