PICK'S FORMULA AND GENERALIZED EHRHART QUASI-POLYNOMIALS

Takayuki Hibi, Miyuki Nakamura, Ivana Natalia Kristantyo Samudro, Akiyoshi Tsuchiya


Abstract


By virtue of Pick's formula, the generalized Ehrhart quasi-polynomial of the triangulation $\mathcal{P} \subset \mathbb{R}^2$ with the vertices $(0,0), (u(n),0), (0,v(n))$, where $u(x)$ and $v(x)$ belong to $\mathbb{Z}[x]$ and where $n=1,2, \ldots$, will be computed.

DOI : http://dx.doi.org/10.22342/jims.21.2.192.71-75


Keywords


generalized Ehrhart quasi-polynomial, Pick's formula

References


M.~Beck and S.~Robins,

``Computing the continuous discretely,''

Springer, 2007

S.~Chen, N.~Li, and S.~V.~Sam,

Generalized Ehrhart polynomials,

textit{Trans. Amer. Math. Soc.}

textbf{364}(2012), 551--569.

R.~P.~Stanley,

``Enumerative Combinatorics, Volume I,''

Second Ed., Cambridge University Press, 2012.


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