312-Avoiding reduced valid hook configurations and duck words

Enumeration of Valid Partial Configurations

Models of configurable products can have hundreds of variables and thousands of configuration constraints. A product engineer usually has a limited responsibility area, and thus is interested in only a small subset of the variables that are relevant to the responsibility area. It is important for the engineer to have an overview of possible products with respect to the responsibility area, with...

Number of cycles in the graph of 312-avoiding permutations

The graph of overlapping permutations is defined in a way analogous to the De Bruijn graph on strings of symbols. However, instead of requiring the tail of one permutation to equal the head of another for them to be connected by an edge, we require that the head and tail in question have their letters appear in the same order of size. We give a formula for the number of cycles of length d in th...

Words Avoiding Reversed Subwords

We examine words w satisfying the following property: if x is a subword of w and |x| is at least k for some fixed k, then the reversal of x is not a subword of w.

Pattern-avoiding alternating words

Abstract. A word w = w1w2 · · ·wn is alternating if either w1 < w2 > w3 < w4 > · · · (when the word is up-down) or w1 > w2 < w3 > w4 < · · · (when the word is down-up). In this paper, we initiate the study of (pattern-avoiding) alternating words. We enumerate up-down (equivalently, down-up) words via finding a bijection with order ideals of a certain poset. Further, we show that the number of 1...

Words Avoiding Abelian Inclusions