q-analogues of Ehrhart polynomials

نویسندگان

چکیده

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

q-analogues of Ehrhart polynomials

One considers weighted sums over points of lattice polytopes, where the weight of a point v is the monomial q for some linear form λ. One proposes a q-analogue of the classical theory of Ehrhart series and Ehrhart polynomials, including Ehrhart reciprocity and involving evaluation at the q-integers.

متن کامل

TWO CURIOUS q-ANALOGUES OF HERMITE POLYNOMIALS

Two well-known q-Hermite polynomials are the continuous and discrete q-Hermite polynomials. In this paper we consider two new q-Hermite polynomials and prove several curious properties about these polynomials. One striking property is the connection with q-Fibonacci polynomials and the recent works on the combinatorics of the Matrix Ansatz of the PASEP.

متن کامل

Generalized Ehrhart Polynomials

Let P be a polytope with rational vertices. A classical theorem of Ehrhart states that the number of lattice points in the dilations P (n) = nP is a quasi-polynomial in n. We generalize this theorem by allowing the vertices of P (n) to be arbitrary rational functions in n. In this case we prove that the number of lattice points in P (n) is a quasi-polynomial for n sufficiently large. Our work w...

متن کامل

Mixed Ehrhart polynomials

For lattice polytopes P1, . . . , Pk ⊆ Rd, Bihan (2016) introduced the discrete mixed volume DMV(P1, . . . , Pk) in analogy to the classical mixed volume. In this note we study the associated mixed Ehrhart polynomial MEP1,...,Pk(n) = DMV(nP1, . . . , nPk). We provide a characterization of all mixed Ehrhart coefficients in terms of the classical multivariate Ehrhart polynomial. Bihan (2016) show...

متن کامل

Characteristic and Ehrhart Polynomials

Let A be a subspace arrangement and let (A; t) be the characteristic polynomial of its intersection lattice L(A). We show that if the subspaces in A are taken from L(Bn), where Bn is the type B Weyl arrangement, then (A; t) counts a certain set of lattice points. This is the only known combinatorial interpretation of this polynomial in the subspace case. One can use this result to study the par...

متن کامل

ذخیره 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: Proceedings of the Edinburgh Mathematical Society

سال: 2015

ISSN: 0013-0915,1464-3839

DOI: 10.1017/s0013091515000243