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Journal of Combinatorial Theory - Series A, 2011 We define a q-analogue of the Calkin–Wilf tree and the Calkin–Wilf sequence. We show that the nth term f(n;q) of the q-analogue of the Calkin–Wilf sequence is the generating function for the number of hyperbinary expansions of n according to the number ...
Toufik Mansour
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Constraining strong c-Wilf equivalence using cluster poset asymptotics
Advances in Applied Mathematics, 2019 Let $π\in \mathfrak{S}_m$ and $σ\in \mathfrak{S}_n$ be permutations. An occurrence of $π$ in $σ$ as a consecutive pattern is a subsequence $σ_i σ_{i+1} \cdots σ_{i+m-1}$ of $σ$ with the same order relations as $π$. We say that patterns $π, τ\in \mathfrak{S}_m$ are strongly c-Wilf equivalent if for all $n$ and $k$, the number of permutations in ...
Mitchell Lee, Ashwin Sah
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The Permutations 123 p 4 … p m and 321 p 4 … p m are Wilf-Equivalent
Graphs and Combinatorics, 2000Write p 1, p 2…p m for the permutation matrix δ pi, j . Let S n (M) be the set of n×n permutation matrices which do not contain the m×m permutation matrix M as a submatrix. In [7] Simion and Schmidt show bijectively that |S n
Eric Babson, Julian West
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Kernel-checked resolution of the last open case (3012 ≡ 3201) of the Hong–Li length-4 Wilf classification on inversion sequences — completing the length-4 classification; fifteen length-5 Wilf equivalences (first classical results at length ≥ 5); and the staircase-prefix invariant (SPI) programme: first distinguishing length, class sizes Σ c!, and the ...
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Enumeration of 2-Wilf Classes of Four 4-letter Patterns
Turkish Journal of Analysis and Number Theory, 2017Toufik Mansour
exaly
Wilf classes for weak ascent sequences avoiding a pair or triple of length-3 patterns
Discrete MathematicsToufik Mansour, David Callan
exaly