0000000000182017
AUTHOR
Phan Thuan Do
The equidistribution of some Mahonian statistics over permutations avoiding a pattern of length three
Abstract We prove the equidistribution of several multistatistics over some classes of permutations avoiding a 3-length pattern. We deduce the equidistribution, on the one hand of inv and foz e ″ statistics, and on the other hand that of maj and makl statistics, over these classes of pattern avoiding permutations. Here inv and maj are the celebrated Mahonian statistics, foz e ″ is one of the statistics defined in terms of generalized patterns in the 2000 pioneering paper of Babson and Steingrimsson, and makl is one of the statistics defined by Clarke, Steingrimsson and Zeng in (1997) [5] . These results solve several conjectures posed by Amini in (2018) [1] .
Exhaustive generation for permutations avoiding (colored) regular sets of patterns
Abstract Despite the fact that the field of pattern avoiding permutations has been skyrocketing over the last two decades, there are very few exhaustive generating algorithms for such classes of permutations. In this paper we introduce the notions of regular and colored regular set of forbidden patterns, which are particular cases of right-justified sets of forbidden patterns. We show the (colored) regularity of several sets of forbidden patterns (some of them involving variable length patterns) and we derive a general framework for the efficient generation of permutations avoiding them. The obtained generating algorithms are based on succession functions, a notion which is a byproduct of t…
Right-Justified Characterization for Generating Regular Pattern Avoiding Permutations
ECO-method and its corresponding succession rules allow to recursively define and construct combinatorial objects. The induced generating trees can be coded by corresponding pattern avoiding permutations. We refine succession rules by using succession functions in case when avoided patterns are regular or c-regular. Although regular patterns are hard to be recognized in general, we give a characterization for its right-justified property which is a prerequisite in the definition of the regular pattern. Based on this characterization, we show the (c-)regularity for various classes of permutations avoiding sets of patterns with variable lengths. Last, the technique of succession functions per…