Generating Function for Bounded Right Suffixes
Abstract
Bounded distinct-entry suffixes avoiding 201 and 210 have a generating function determined by binary choices.
Theorem 1.1 (Enumeration by the first label).
Lean statement: D5/S3/Combinatorics/InversionSeq/InversionSeq152SuffixSeries.first_label_suffix_enumeration
Proof. Machine-checked in Lean as D5/S3/Combinatorics/InversionSeq/InversionSeq152SuffixSeries.first_label_suffix_enumeration (✓ std3). ∎
Source. Repository-derived.
Acknowledgement. David Callan, Toufik Mansour (2023). Inversion Sequences Avoiding Quadruple Length-3 Patterns. DOI: 10.5281/zenodo.8399694. URL: https://math.colgate.edu/~integers/x78/x78.pdf.
Commentary.
Fix nonnegative integers l and h. Over the rational numbers, let S(x) have constant coefficient one and, in each positive degree n, the number of words of length n with pairwise distinct entries, all greater than l, avoiding 201 and 210 and satisfying the bound that the entry at position i is at most l + h + 1 + i, with positions numbered from zero. Let B(x) have coefficient 2 to the power n in degree n. Then 2 (1 - x) S(x) = 1 + B(x) to the power h.
References
- Truth anchor:
D5/S3/Combinatorics/InversionSeq/InversionSeq152SuffixSeries.first_label_suffix_enumeration - Dependency: D5/S3/Combinatorics/InversionSeq/InversionSeq152Labels
- Dependency: D5/S3/Combinatorics/InversionSeq/InversionSeq152Multiplicity