Wilf equivalences between vincular patterns in inversion sequences
نویسندگان
چکیده
Inversion sequences are finite of non-negative integers, where the value each entry is bounded from above by its position. They provide a useful encoding permutations. Patterns in inversion have been studied Corteel–Martinez–Savage–Weselcouch and Mansour–Shattuck classical case, patterns can occur any positions, Auli–Elizalde consecutive only adjacent entries form an occurrence pattern. These papers classify length 3 into Wilf equivalence classes according to number avoiding them. In this paper we consider vincular sequences, which, analogy Babson–Steingrímsson permutations, require certain be adjacent, thus generalize both patterns. Solving three conjectures Lin Yan, complete classification classes, more restrictive that occurrences pattern positions such occurrences. We find first known instance these two do not coincide.
منابع مشابه
Shape-wilf-equivalences for Vincular Patterns
We extend the notion of shape-Wilf-equivalence to vincular patterns (also known as “generalized patterns” or “dashed patterns”). First we introduce a stronger equivalence on patterns which we call filling-shape-Wilfequivalence. When vincular patterns α and β are filling-shape-Wilf-equivalent, we prove that α⊕ σ and β ⊕ σ must also be filling-shape-Wilf-equivalent. We also discover two new pairs...
متن کاملSome Wilf-equivalences for Vincular Patterns
We prove several Wilf-equivalences for vincular patterns of length 4, some of which generalize to infinite families of vincular patterns. We also present functional equations for the generating functions for the number of permutations of length n avoiding σ for the patterns 124-3, 134-2, 231-4, 241-3, 132-4, and 142-3. This nearly completes the Wilfclassification of vincular patterns of length ...
متن کاملEnumeration schemes for vincular patterns
We extend the notion of an enumeration scheme developed by Zeilberger and Vatter to the case of vincular patterns (also called “generalized patterns” or “dashed patterns”). In particular we provide an algorithm which takes in as input a set B of vincular patterns and search parameters and returns a recurrence (called a “scheme”) to compute the number of permutations of length n avoiding B or co...
متن کاملOperators of Equivalent Sorting Power and Related Wilf-equivalences
We study sorting operators A on permutations that are obtained composing Knuth’s stack sorting operator S and the reversal operator R, as many times as desired. For any such operator A, we provide a size-preserving bijection between the set of permutations sorted by S ◦ A and the set of those sorted by S ◦ R ◦ A, proving that these sets are enumerated by the same sequence, but also that many cl...
متن کاملPatterns in Inversion Sequences II: Inversion Sequences Avoiding Triples of Relations
Inversion sequences of length n, In, are integer sequences (e1, . . . , en) with 0 ≤ ei < i for each i. The study of patterns in inversion sequences was initiated recently by Mansour-Shattuck and Corteel-Martinez-Savage-Weselcouch through a systematic study of inversion sequences avoiding words of length 3. We continue this investigation by reframing the notion of a length-3 pattern from a “wor...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Applied Mathematics and Computation
سال: 2021
ISSN: ['1873-5649', '0096-3003']
DOI: https://doi.org/10.1016/j.amc.2020.125514