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Tomie Masaya

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Hamiltonian cycles for the square of the augmentation graphs and Gray codes for restricted permutations and ascent sequences

Tomie Masaya
12 Dec 2016 math.CO arxiv.org/abs/1612.03620

In this paper, we construct a listing for the vertices of the augmentation graph of given size, and as a consequence, we obtain a Hamiltonian cycle for the square of the augmentation graph of given size. As applications, we have a Gray code for the $132$-$312$ avoiding permutations of given length such that two successive permutations differ by at most $2$ adjacent transpositions. Also we obtain Gray codes of strong distance $2$ for the $001$ avoiding ascent sequences and the $010$ avoiding ascent sequences of given length.

A relation between the shape of a permutation and the shape of the base poset derived from the Lehmer codes

Tomie Masaya
13 Nov 2011 math.CO arxiv.org/abs/1111.3094

For a permutation $\omega \in S_{n}$ Denoncourt constructed a poset $M_{\omega}$ which is the set of join-irreducibles of the Lehmer codes of the permutations in $[e, \omega]$ in the inversion order on $S_{n}$. In this paper we show that $M_{\omega}$ is a $B_{2}$-free poset if and only if $\omega$ is a 3412-3421-avoiding permutation.

NBB bases of some pattern avoiding lattices

Tomie Masaya
22 Dec 2009 math.CO arxiv.org/abs/0912.4560

In this paper we will determine the NBB bases with respect to standard ordering of coatoms (resp.atoms) of 123-132-213-avoiding (resp.321-avoiding) lattices. Using these expression we will calculate the M\"obius numbers of 123-132-213-avoiding lattices and 321-avoiding lattices. These values become some modification of fibonacci polynomials.

M\"obius numbers of some modified generalized noncrossing partitions

Tomie Masaya
11 May 2009 math.CO arxiv.org/abs/0905.1660

In this paper we will give a M\"obius number of $NC^{k}(W) \setminus \bf{mins} \cup {\hat{0} }$ for a Coxeter group $W$ which contains an affirmative answer for the conjecture 3.7.9 in Armstrong's paper [ Generalized noncrossing partitions and combinatorics of Coxeter groups. arXiv:math/0611106].

A generalization of Chebyshev polynomials and non rooted posets

Tomie Masaya
05 Apr 2007 math.CO arxiv.org/abs/0704.0685

In this paper we give a generalization of Chebyshev polynomials and using this we describe the M\"obius function of the generalized subword order from a poset {a1,...as,c |ai<c}, which contains an affirmative answer for the conjecture by Bj\"orner, Sagan, Vatter.[5,10]