Quang T. Bach

most citedGenerating functions for permutations which avoid consecutive patterns with multiple descents

1 citations · 1 across the 5 of their papers we have counts for

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5 papers

math.CO2017★ 1 cited

Generating functions for permutations which avoid consecutive patterns with multiple descents

Quang T. Bach, Jeffrey B. Remmel

Let $S_{n}$ denote the group all permutations of $n$ . For every permutation $σ$ , we let $des (σ)$ denote the number of descents in $σ$ and $LRMin (σ)$ denote the numb…

math.CO2017

Q-analogues of the Fibo-Stirling numbers

Quang T. Bach, Roshil Paudyal, Jeffrey B. Remmel

Let $F_{n}$ denote the $n^{t h}$ Fibonacci number relative to the initial conditions $F_{0} = 0$ and $F_{1} = 1$ . Bach, Paudyal, and Remmel introduced Fibonacci analogues of the Stirling numb…

math.CO2015

Generating functions for descents over permutations which avoid sets of consecutive patterns

Quang T. Bach, Jeffrey B. Remmel

We extend the reciprocity method of Jones and Remmel to study generating functions of the form $$\sum_{n \geq 0} \frac{t^n}{n!} \sum_{σ\in \mathcal{NM}_n(Γ)}x^{\mathrm{LRmin}(σ)}y^…

math.CO2015

Descent c-Wilf Equivalence

Quang T. Bach, Jeffrey B. Remmel

Let $S_{n}$ denote the symmetric group. For any $σ \in S_{n}$ , we let $des (σ)$ denote the number of descents of $σ$ , $inv (σ)$ denote the number of inversions of $σ$ , a…

math.CO2015

A Fibonacci analogue of Stirling numbers

Quang T. Bach, Roshil Paudyal, Jeffrey B. Remmel

Consider the Fibonacci numbers defined by setting $F_{1} = 1 = F_{2}$ and $F_{n} = F_{n - 1} + F_{n - 2}$ for $n \geq 3$ . We let $n_{F}! = F_{1} \dots F_{n}$ and $\binom{n}{k}_F = \frac{n_F!}{k_F!(n-k)_…